Frank Duzaar

Prof. Dr. Frank Duzaar

Faculty of Sciences
Department of Data Science (DDS)

Room 02.348
Cauerstraße 11
91058 Erlangen

Phone number: +49 9131 85-67101
Fax number: +49 9131 85-67100
Email: frank.duzaar@fau.de
Website: https://www.datascience.nat.fau.eu/frank-duzaar

Professor Dr. Frank Duzaar has been retired since 01.04.2023.

Since then, he has been working as a visiting professor at Paris Lodron University Salzburg.

Publications

Boegelein V., Duzaar F., Marcellini P., Scheven C.:
Boundary regularity for elliptic systems with p, q-growth
In: Journal De Mathematiques Pures Et Appliquees 159 (2022), p. 250-293
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2021.12.004
Bögelein V., Duzaar F., Giova R., Passarelli di Napoli A.:
Higher regularity in congested traffic dynamics
In: Mathematische Annalen (2022)
ISSN: 0025-5831
DOI: 10.1007/s00208-022-02375-y
Bögelein V., Duzaar F., Liao N., Scheven C.:
Boundary regularity for parabolic systems in convex domains
In: Journal of the London Mathematical Society-Second Series (2022)
ISSN: 0024-6107
DOI: 10.1112/jlms.12545
Bögelein V., Duzaar F., Liao N., Scheven C.:
Gradient Hölder regularity for degenerate parabolic systems
In: Nonlinear Analysis - Theory Methods & Applications 225 (2022), Article No.: 113119
ISSN: 0362-546X
DOI: 10.1016/j.na.2022.113119

Bögelein V., Duzaar F., Liao N.:
On the Hölder regularity of signed solutions to a doubly nonlinear equation
In: Journal of Functional Analysis 281 (2021), Article No.: 109173
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2021.109173

Bogelein V., Dacorogna B., Duzaar F., Marcellini P., Scheven C.:
Integral convexity and parabolic systems
In: SIAM Journal on Mathematical Analysis 52 (2020), p. 1489-1525
ISSN: 0036-1410
DOI: 10.1137/19M1287870
Bögelein V., Duzaar F., Kinnunen J., Scheven C.:
Higher integrability for doubly nonlinear parabolic systems
In: Journal De Mathematiques Pures Et Appliquees 9 (2020), p. 31–72
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2020.06.009
URL: https://arxiv.org/abs/1810.06039

Agricola I., Bögelein V., Duzaar F.:
In memoriam Thomas Friedrich (1949–2018).
In: Annals of Global Analysis and Geometry 56 (2019), p. 613-630
ISSN: 0232-704X
DOI: 10.1007/s10455-019-09692-7
URL: https://link.springer.com/article/10.1007/s10455-019-09692-7
Bögelein V., Duzaar F., Scheven C.:
Higher integrability for the singular porous medium system
In: Journal für die reine und angewandte Mathematik (2019), p. 203-230
ISSN: 0075-4102
DOI: 10.1515/crelle-2019-0038
URL: https://www.degruyter.com/document/doi/10.1515/crelle-2019-0038/html
Bögelein V., Duzaar F., Schätzler L., Scheven C.:
Existence for evolutionary problems with linear growth by stability methods
In: Journal of Differential Equations 266 (2019), p. 7709-7748
ISSN: 0022-0396
DOI: 10.1016/j.jde.2018.12.012

Bögelein V., Duzaar F., Korte R., Scheven C.:
The higher integrability of weak solutions of porous medium systems
In: Advances in Nonlinear Analysis (2018)
ISSN: 2191-9496
DOI: 10.1515/anona-2017-0270
URL: https://www.degruyter.com/view/j/anona.ahead-of-print/anona-2017-0270/anona-2017-0270.xml
Bögelein V., Duzaar F., Marcellini P., Scheven C.:
A variational approach to doubly nonlinear equations
In: Rendiconti Lincei. Matematica e Applicazioni 29 (2018), p. 739--772
ISSN: 1120-6330
DOI: 10.4171/RLM/832
Bögelein V., Duzaar F., Marcellini P., Scheven C.:
Doubly nonlinear equations of porous medium type
In: Archive for Rational Mechanics and Analysis 229 (2018), p. 503--545
ISSN: 0003-9527
DOI: 10.1007/s00205-018-1221-9
Bögelein V., Duzaar F., Scheven C., Singer T.:
Existence of variational solutions in noncylindrical domains
In: SIAM Journal on Mathematical Analysis 50 (2018), p. 3007--3057
ISSN: 0036-1410
DOI: 10.1137/17M1156423

Bögelein V., Duzaar F., Fusco N.:
A quantitative isoperimetric inequality on the sphere
In: Advances in Calculus of Variations 10 (2017), p. 223--265
ISSN: 1864-8258
DOI: 10.1515/acv-2015-0042
Bögelein V., Duzaar F., Marcellini P., Signoriello S.:
Parabolic equations and the bounded slope condition
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 34 (2017), p. 355--379
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2015.12.005
Bögelein V., Duzaar F., Scheven C.:
The obstacle problem for parabolic minimizers
In: Journal of Evolution Equations 17 (2017), p. 1273--1310
ISSN: 1424-3199
DOI: 10.1007/s00028-017-0384-4

Bögelein V., Duzaar F., Gianazza U.:
Sharp boundedness and continuity results for the singular porous medium equation
In: Israel Journal of Mathematics 214 (2016), p. 259--314
ISSN: 0021-2172
DOI: 10.1007/s11856-016-1360-3
Bögelein V., Duzaar F., Scheven C.:
The obstacle problem for the total variation flow
In: Annales Scientifiques De L Ecole Normale Superieure 49 (2016), p. 1143--1188
ISSN: 0012-9593
DOI: 10.24033/asens.2306
Bögelein V., Duzaar F., Scheven C.:
The total variation flow with time dependent boundary values
In: Calculus of Variations and Partial Differential Equations 55 (2016), p. Art. 108, 31
ISSN: 0944-2669
DOI: 10.1007/s00526-016-1041-4

Bögelein V., Duzaar F., Fusco N.:
A sharp quantitative isoperimetric inequality in higher codimension
In: ATTI Della Accademia Nazionale Dei Lincei Rendiconti Lincei Scienze Fisiche e Naturali 26 (2015), p. 309-362
ISSN: 1120-6349
DOI: 10.4171/RLM/709
Bögelein V., Duzaar F., Gianazza U.:
VERY WEAK SOLUTIONS OF SINGULAR POROUS MEDIUM EQUATIONS WITH MEASURE DATA
In: Communications on Pure and Applied Analysis 14 (2015), p. 23-49
ISSN: 1534-0392
DOI: 10.3934/cpaa.2015.14.23
Bögelein V., Duzaar F., Marcellini P.:
A Time Dependent Variational Approach to Image Restoration
In: Siam Journal on Imaging Sciences 8 (2015), p. 968-1006
ISSN: 1936-4954
DOI: 10.1137/140992771
Bögelein V., Duzaar F., Marcellini P., Signoriello S.:
Non local diffusion equations
In: Journal of Mathematical Analysis and Applications 432 (2015), p. 398-428
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.06.053
Bögelein V., Duzaar F., Scheven C.:
A sharp quantitative isoperimetric inequality in hyperbolic n-space
In: Calculus of Variations and Partial Differential Equations 54 (2015), p. 3967-4017
ISSN: 0944-2669
DOI: 10.1007/s00526-015-0928-9
Bögelein V., Duzaar F., Scheven C.:
Short-Time Regularity for the H-Surface Flow
In: International Mathematics Research Notices (2015), p. 3694-3750
ISSN: 1073-7928
DOI: 10.1093/imrn/rnu042
Duzaar F., Scheven C.:
The evolution of H-surfaces with a Plateau boundary condition
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 32 (2015), p. 109-157
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2013.10.003

Bögelein V., Duzaar F., Gianazza U.:
Continuity estimates for porous medium type equations with measure data
In: Journal of Functional Analysis 267 (2014), p. 3351-3396
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2014.08.014
Bögelein V., Duzaar F., Marcellini P.:
Existence of evolutionary variational solutions via the calculus of variations
In: Journal of Differential Equations 256 (2014), p. 3912-3942
ISSN: 0022-0396
DOI: 10.1016/j.jde.2014.03.005

Bögelein V., Duzaar F., Gianazza U.:
POROUS MEDIUM TYPE EQUATIONS WITH MEASURE DATA AND POTENTIAL ESTIMATES
In: SIAM Journal on Mathematical Analysis 45 (2013), p. 3283-3330
ISSN: 0036-1410
DOI: 10.1137/130925323
Bögelein V., Duzaar F., Marcellini P.:
Parabolic equations with (p,q)-growth
In: Journal De Mathematiques Pures Et Appliquees 100 (2013), p. 535-563
ISSN: 0021-7824
Bögelein V., Duzaar F., Marcellini P.:
Parabolic Systems with p, q-Growth: A Variational Approach
In: Archive for Rational Mechanics and Analysis 210 (2013), p. 219-267
ISSN: 0003-9527
DOI: 10.1007/s00205-013-0646-4
Bögelein V., Duzaar F., Mingione G.:
The regularity of general parabolic systems with degenerate diffusions
In: Memoirs of the American Mathematical Society 221 (2013)
ISSN: 0065-9266
DOI: 10.1090/S0065-9266-2012-00664-2
Bögelein V., Duzaar F., Scheven C.:
Weak solutions to the heat flow for surfaces of prescribed mean curvature
In: Transactions of the American Mathematical Society 365 (2013), p. 4633-4677
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-2013-05885-0

Bögelein V., Duzaar F.:
Holder estimates for parabolic p(x, t)-Laplacian systems
In: Mathematische Annalen 354 (2012), p. 907-938
ISSN: 0025-5831
DOI: 10.1007/s00208-011-0750-4
Bögelein V., Duzaar F., Habermann J., Scheven C.:
Stationary electro-rheological fluids: Low order regularity for systems with discontinuous coefficients
In: Advances in Calculus of Variations 5 (2012), p. 1-57
ISSN: 1864-8258
DOI: 10.1515/ACV.2011.009
Bögelein V., Duzaar F., Scheven C.:
Global solutions to the heat flow for m-harmonic maps and regularity
In: Indiana University Mathematics Journal 61 (2012), p. 2157-2210
ISSN: 0022-2518
URL: http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=4819&year=2012&volume=61
Duzaar F., Habermann J.:
Partial regularity for parabolic systems with non-standard growth
In: Journal of Evolution Equations 12 (2012), p. 203-244
ISSN: 1424-3199
DOI: 10.1007/s00028-011-0130-2

Bögelein V., Duzaar F.:
Higher integrability for parabolic systems with non-standard growth and degenerate diffusions
In: Publicacions Matematiques 55 (2011), p. 201-250
ISSN: 0214-1493
DOI: 10.5565/PUBLMAT_55111_10
URL: http://www.mat.uab.es/pubmat/volums/navegador/volum_id:89#
Bögelein V., Duzaar F., Habermann J., Scheven C.:
Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients
In: Proceedings of the London Mathematical Society 103 (2011), p. 371-404
ISSN: 0024-6115
DOI: 10.1112/plms/pdr009
URL: http://plms.oxfordjournals.org/content/early/2011/02/27/plms.pdr009.abstract
Bögelein V., Duzaar F., Mingione G.:
Degenerate problems with irregular obstacles
In: Journal für die reine und angewandte Mathematik 650 (2011), p. 107-160
ISSN: 0075-4102
DOI: 10.1515/CRELLE.2011.006
URL: http://www.reference-global.com/doi/abs/10.1515/CRELLE.2011.006
Duzaar F., Mingione G.:
Gradient estimates via non-linear potentials
In: American Journal of Mathematics 133 (2011), p. 1093-1149
ISSN: 0002-9327
DOI: 10.1353/ajm.2011.0023
URL: http://muse.jhu.edu/login?uri=/journals/american_journal_of_mathematics/v133/133.4.duzaar.pdf
Duzaar F., Mingione G., Steffen K.:
Parabolic systems with polynomial growth and regularity
In: Memoirs of the American Mathematical Society 214 (2011), p. -
ISSN: 0065-9266
DOI: 10.1090/S0065-9266-2011-00614-3
URL: http://www.ams.org/journals/memo/0000-000-00/S0065-9266-2011-00614-3/home.html

Bögelein V., Duzaar F., Mingione G.:
The boundary regularity of non-linear parabolic systems I
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 27 (2010), p. 201-255
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2009.09.003
Bögelein V., Duzaar F., Mingione G.:
The boundary regularity of non-linear parabolic systems II
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 27 (2010), p. 145-200
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2009.09.002
URL: https://www.sciencedirect.com/science/article/pii/S0294144909000833?via=ihub
Duzaar F., Mingione G.:
Gradient continuity estimates
In: Calculus of Variations and Partial Differential Equations 39 (2010), p. 379-418
ISSN: 0944-2669
DOI: 10.1007/s00526-010-0314-6
Duzaar F., Mingione G.:
Gradient estimates via linear and nonlinear potentials
In: Journal of Functional Analysis 259 (2010), p. 2961-2998
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2010.08.006
Duzaar F., Mingione G.:
Local Lipschitz regularity for degenerate elliptic systems
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 27 (2010), p. 1361-1396
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2010.07.002

Duzaar F., Mingione G.:
Gradient estimates in non-linear potential theory
In: Rendiconti Lincei. Matematica e Applicazioni 20 (2009), p. 179-190
ISSN: 1120-6330
DOI: 10.4171/RLM/540
URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=20&iss=2&rank=6
Duzaar F., Mingione G.:
Harmonic Type Approximations Lemmas
In: Journal of Mathematical Analysis and Applications 352 (2009), p. 301-335
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.09.076

Duzaar F., Kristensen J., Mingione G.:
The existence of regular boundary points for nonlinear elliptic systems. To the memory of Sergio Campanato
In: Journal für die reine und angewandte Mathematik 2007 (2007), p. 17-58
ISSN: 0075-4102
DOI: 10.1515/CRELLE.2007.002
URL: http://www.reference-global.com/doi/pdf/10.1515/CRELLE.2007.002

Duzaar F.:
Optimal regularity for second order parabolic systems via $A$-caloric approximation
In: Rivista di matematica della Università di Parma 7 (2005), p. 91-113
ISSN: 0035-6298
URL: http://rivista.math.unipr.it/vols/2005-4s/04.html
Duzaar F., Grotowski JF., Kronz M.:
Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth
In: Annali Di Matematica Pura Ed Applicata 184 (2005), p. 421-448
ISSN: 0373-3114
DOI: 10.1007/s10231-004-0117-5
URL: http://www.springerlink.com/content/vcrdegy4y8j1b1px/fulltext.pdf
Duzaar F., Mingione G.:
Second order parabolic systems, optimal regularity, and singular sets of solutions
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 22 (2005), p. 705-751
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2004.10.011
URL: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VKB-4G4PC1B-1-8&_cdi=6118&_user=616145&_orig=search&_coverDate=12%2F31%2F2005&_sk=999779993&view=c&wchp=dGLbVzb-zSkWz&md5=6e5a844d72a331ada8ce3e8dff936583&ie=/sdarticle.pdf

Duzaar F., Gastel A., Mingione G.:
Elliptic systems, singular sets and Dini continuity
In: Communications in Partial Differential Equations 29 (2004), p. 1215-1240
ISSN: 0360-5302
DOI: 10.1081/PDE-200033734
URL: http://www.informaworld.com/smpp/content~db=all?content=10.1081/PDE-200033734
Duzaar F., Grotowski JF., Kronz M.:
Partial and full boundary regularity for minimizers of functionals with nonquadratic growth
In: Journal of Convex Analysis 11 (2004), p. 437-476
ISSN: 0944-6532
URL: http://www.heldermann.de/JCA/JCA11/jca11027.htm
Duzaar F., Mingione G.:
Regularity for degenerate elliptic problems via $p$-harmonic approximation
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 21 (2004), p. 735-766
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2003.09.003
URL: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VKB-4BRBCVJ-1-5&_cdi=6118&_user=616145&_orig=search&_coverDate=10%2F31%2F2004&_sk=999789994&view=c&wchp=dGLzVlz-zSkzS&md5=e353b7aee2d2bf8cde5892ba0f08fc99&ie=/sdarticle.pdf
Duzaar F., Mingione G.:
The $p$-harmonic approximation and the regularity of $p$-harmonic maps
In: Calculus of Variations and Partial Differential Equations 20 (2004), p. 235-256
ISSN: 0944-2669
DOI: 10.1007/s00526-003-0233-x
URL: http://www.springerlink.com/content/97wh09at0y84v6dj/fulltext.pdf

Duzaar F., Gastel A.:
Nonlinear elliptic systems with Dini continuous coefficients
In: Archiv der Mathematik 78 (2002), p. 58-73
ISSN: 0003-889X
DOI: 10.1007/s00013-002-8217-1
URL: http://www.springerlink.com/content/ubwra8e6wemxr1m5/fulltext.pdf
Duzaar F., Kronz M.:
Regularity of $\omega$-minimizers of quasi-convex variational integrals with polynomial growth
In: Differential Geometry and its Applications 17 (2002), p. 139-152
ISSN: 0926-2245
DOI: 10.1016/S0926-2245(02)00104-3
URL: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TYY-46B4N65-4-B3&_cdi=5631&_user=616145&_orig=search&_coverDate=09%2F30%2F2002&_sk=999829997&view=c&wchp=dGLbVtz-zSkzV&md5=04f186a6d48102cbdc0bdf90fa2a463e&ie=/sdarticle.pdf
Duzaar F., Steffen K.:
Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals
In: Journal für die reine und angewandte Mathematik 546 (2002), p. 73-138
ISSN: 0075-4102
DOI: 10.1515/crll.2002.046
URL: http://www.reference-global.com/doi/pdf/10.1515/crll.2002.046

Duzaar F., Gastel A., Grotowski JF.:
Optimal partial regularity for nonlinear elliptic systems of higher order
In: Journal of Mathematical Sciences - the University of Tokyo 8 (2001), p. 463-499
ISSN: 1340-5705
URL: http://journal.ms.u-tokyo.ac.jp/

Duzaar F., Gastel A., Grotowski JF.:
Partial regularity for almost minimizers of quasi-convex integrals
In: SIAM Journal on Mathematical Analysis 32 (2000), p. 665-687
ISSN: 0036-1410
DOI: 10.1137/S0036141099374536
URL: http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJMAAH000032000003000665000001&idtype=cvips&gifs=yes
Duzaar F., Grotowski JF.:
Existence and regularity for higher dimensional $H$-systems
In: Duke Mathematical Journal 101 (2000), p. 459-485
ISSN: 0012-7094
URL: http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdffirstpage_1&handle=euclid.dmj/1092749201
Duzaar F., Grotowski JF.:
Optimal interior partial regularity for nonlinear elliptic systems: The method of $A$-harmonic approximation
In: Manuscripta Mathematica 103 (2000), p. 267-298
ISSN: 0025-2611
DOI: 10.1007/s002290070007
URL: http://www.springerlink.com/content/jvxdcub8hywkpyd5/fulltext.pdf

Duzaar F., Steffen K.:
Parametric sufaces of least $H$-energy in a Riemannian manifold
In: Mathematische Annalen 314 (1999), p. 197-244
ISSN: 0025-5831
URL: http://www.springerlink.com/content/ywgd2yf1t8elu9vp/fulltext.pdf

Duzaar F., Gastel A.:
Minimizing $p$-harmonic maps at a free boundary
In: Bollettino della Unione Matematica Italiana B 1 (1998), p. 391-406
ISSN: 0392-4041
Duzaar F., Kuwert E.:
Minimization of conformally invariant energies in homotopy classes
In: Calculus of Variations and Partial Differential Equations 6 (1998), p. 285-313
ISSN: 0944-2669
DOI: 10.1007/s005260050092
URL: http://www.springerlink.com/content/xlb84df4mpc08qme/fulltext.pdf

Duzaar F., Steffen K.:
Boundary regularity for area minimizing currents with prescribed volume
In: Journal of Geometric Analysis 7 (1997), p. 585-592
ISSN: 1050-6926
DOI: 10.1007/BF02921634
URL: http://springerlink.com/content/pm75t747g33g7097/fulltext.pdf

Duzaar F.:
Hypersurfaces with constant mean curvature and prescribed area
In: Manuscripta Mathematica 91 (1996), p. 303-315
ISSN: 0025-2611
DOI: 10.1007/BF02567956
URL: http://www.springerlink.com/content/03k827467654842w/fulltext.pdf
Duzaar F., Grotowski JF.:
A mixed boundary value problem for energy minimizing harmonic maps
In: Mathematische Zeitschrift 221 (1996), p. 153-167
ISSN: 0025-5874
DOI: 10.1007/BF02622105
URL: http://www.springerlink.com/content/m26h54512503k505/fulltext.pdf
Duzaar F., Steffen K.:
Existence of hypersurfaces with prescribed mean curvature in Riemannian manifolds
In: Indiana University Mathematics Journal 45 (1996), p. 1045-1093
ISSN: 0022-2518
DOI: 10.1512/iumj.1996.45.1117
URL: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/1996/45/1117

Duzaar F., Fuchs M.:
Existence of area minimizing tangent cones of integral currents with prescribed mean curvature
In: Acta Mathematica Scientia 15 (1995), p. 95-102
ISSN: 0252-9602
URL: http://en.cnki.com.cn/Article_en/CJFDTotal-SXWY501.011.htm

Duzaar F.:
Existence and regularity of hypersurfaces with prescribed mean curvature and a free boundary
In: Journal für die reine und angewandte Mathematik 457 (1994), p. 23-43
ISSN: 0075-4102
URL: https://eudml.org/doc/153669
Duzaar F., Grotowski JF.:
Energy minimizing harmonic maps with an obstacle at the free boundary
In: Manuscripta Mathematica 83 (1994), p. 291-314
ISSN: 0025-2611
DOI: 10.1007/BF02567615
URL: http://www.springerlink.com/content/m67p822218012813/fulltext.pdf
Duzaar F., Steffen K.:
Comparison principles for hypersurfaces of prescribed mean curvature
In: Journal für die reine und angewandte Mathematik 457 (1994), p. 71-83
ISSN: 0075-4102
URL: http://eudml.org/doc/153671

Duzaar F.:
On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 10 (1993), p. 191-214
ISSN: 0294-1449
URL: http://www.numdam.org/item?id=AIHPC_1993__10_2_191_0
Duzaar F., Steffen K.:
$\lambda$ minimizing currents
In: Manuscripta Mathematica 80 (1993), p. 403-447
ISSN: 0025-2611
DOI: 10.1007/BF03026561
Duzaar F., Steffen K.:
Boundary regularity for minimizing currents with prescribed mean curvature
In: Calculus of Variations and Partial Differential Equations 1 (1993), p. 355-406
ISSN: 0944-2669
DOI: 10.1007/BF01206958
URL: http://www.springerlink.com/content/v82680827q00q040/fulltext.pdf

Duzaar F., Fuchs M.:
A general existence theorem for integral currents with prescribed mean curvature form
In: Bollettino della Unione Matematica Italiana B 6 (1992), p. 901-912
ISSN: 0392-4041
Duzaar F., Steffen K.:
Area minimizing hypersurfaces with prescribed volume and boundary
In: Mathematische Zeitschrift 209 (1992), p. 581-618
ISSN: 0025-5874
DOI: 10.1007/BF02570855
URL: http://www.springerlink.com/content/t483384625752883/fulltext.pdf

Duzaar F.:
Regularity of $p$-harmonic maps into a closed hemisphere
In: Bollettino della Unione Matematica Italiana B 5 (1991), p. 157-170
ISSN: 0392-4041
Duzaar F., Fuchs M.:
Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmung
In: Zeitschrift für Analysis und ihre Anwendungen 10 (1991), p. 525-534
ISSN: 0232-2064
Duzaar F., Fuchs M.:
Einige Bemerkungen über die Regularität von stationären Punkten gewisser geometrischer Variationsintegrale
In: Mathematische Nachrichten 152 (1991), p. 39-47
ISSN: 0025-584X
URL: http://www3.interscience.wiley.com/cgi-bin/fulltext/113459912/PDFSTART
Duzaar F., Fuchs M.:
Existence and regularity of functions which minimize certain energies in homotopy classes of mappings
In: Asymptotic Analysis 5 (1991), p. 129-144
ISSN: 0921-7134
Duzaar F., Fuchs M.:
On integral currents with constant mean curvature
In: Rendiconti Del Seminario Matematico Della Universita Di Padova 85 (1991), p. 79-103
ISSN: 0041-8994
URL: http://rendiconti.math.unipd.it/volumes/vol085.html?lan=english

Duzaar F., Fuchs M.:
Existenz und Regularität von Hyperflächen mit vorgeschriebener mittlerer Krümmung
In: Analysis 10 (1990), p. 193-230
ISSN: 0003-2638
Duzaar F., Fuchs M.:
On removable singularities of p-harmonic maps
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 7 (1990), p. 385-405
ISSN: 0294-1449
Duzaar F., Fuchs M.:
On the existence of integral currents with prescribed mean curvature vector
In: Manuscripta Mathematica 67 (1990), p. 41-67
ISSN: 0025-2611
DOI: 10.1007/BF02568422
URL: http://www.springerlink.com/content/f87239377k748433/fulltext.pdf

Duzaar F., Steffen K.:
An optimal estimate for the singular set of a harmonic map in the free boundary
In: Journal für die reine und angewandte Mathematik 401 (1989), p. 157-187
ISSN: 1435-5345
Duzaar F., Steffen K.:
A partial regularity theorem for harmonic maps at a free boundary
In: Asymptotic Analysis 2 (1989), p. 299-343
ISSN: 0921-7134
URL: http://www.iospress.nl/loadtop/load.php?isbn=09217134

Duzaar F.:
Variational inequalities and harmonic mappings
In: Journal für die reine und angewandte Mathematik 374 (1987), p. 39-60
ISSN: 1435-5345

Duzaar F., Fuchs M.:
Optimal regularity theorems for variational problems with obstacles
In: Manuscripta Mathematica 56 (1986), p. 209-234
ISSN: 0025-2611
URL: http://www.springerlink.com/content/g6776qu144261x42/fulltext.pdf
Duzaar F., Fuchs M.:
Variational problems with non-convex obstacles and an integral constraint for vector-valued functions
In: Mathematische Zeitschrift 191 (1986), p. 585-591
ISSN: 0025-5874
URL: http://www.springerlink.com/content/jl471u5686011245/fulltext.pdf

Projects

Term: 1. May 2020 - 30. June 2022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)

The subproject ist concerned with stability questions for the non stationary gas flow in gas networks, which is described by the friction dominated ISO-3 model. From the analytical point of view the model consists in a system of nonlinear parabolic partial differential equations which can be transformed into a doubly nonlinear degenerate parabolic equation. We focus on stability issues for the (weak) solution (in the parabolic Sobolev space) with respect to variations of structural parameters and initial-boundary data. In particular, we expect results for the ISO-3 model concerning the stability under variations of friction parameters and the underlying gas model (ideal or real gas).

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Term: 1. July 2010 - 30. July 2013
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: Frank Duzaar

Prof. Dr. Frank Duzaar

Ziel des Projektes ist einerseits die Entwicklung einer Caldcrón & Zygmund-Theorie für Lösungen elliptischer und parabolischer Hindernis-Probleme für partielle Differentialoperatoren in Divergenzform vom p-LapIace Typ, und andererseits die Herleitung punktweiser Potential-Abschätzungen der Lösungen in Termen des Hindernisses. Angestrebt wird der Beweis einer klassischen Calderón & Zygmund-Abschätzung für den räumlichen Gradienten der Lösung in Termen der Integrabilität des Hindernisses. Genauer sol…

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Term: 26. July 2006 - 31. December 2009
Funding source: DFG-Einzelförderung / Heisenberg-Programm (EIN-HEI)
Project leader: Frank Duzaar

Prof. Dr. Frank Duzaar

Für schwache Lösungen subelliptischer Gleichungen in der Heisenberg-Gruppe, deren Koeffizienten einer superlinearen Nichtstandard-Wachstumsbedingung genügen, soll unter natürlichen Restriktionen an das Wachstum der Koeffizienten die lokale Regularität, d.h. die Glattheit der Lösungen, gezeigt werden. Die Einschränkungen werden dabei in Abhängigkeit von der Dimension an das Wachstum der Koeffizienten von oben zu stellen sein (nach unten wird der Einfachheit halber lineares Wachstum der Koeffizienten angenom…

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Term: 1. January 1998 - 31. December 2000
Funding source: Deutsche Forschungsgemeinschaft (DFG)
Project leader: Frank Duzaar

Prof. Dr. Frank Duzaar

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Curriculum Vitae

Dr. Frank Duzaar, born 19.02.1957 in Krefeld, Germany

Scientific Vita

05/2000 – 03/2023	Full Professor (C4), Friedrich-Alexander University Erlangen-Nürnberg
08/1999	Offer of Full Professorship (C4), Otto-von-Guericke-Universität Magdeburg
10/1995 – 04/2000	Associate Professor (C3), Humboldt-Universität zu Berlin
05/1993 – 09/1995	Associate Professor (C2), Rheinische Friedrich-Wilhelms-Universität Bonn
06/1991	Habilitation in Mathematics, Heinrich-Heine-Universität Düsseldorf
06/1985	Completed Ph.D., Department of Mathematics, Heinrich-Heine-Universität Düsseldorf
1982	Diploma in Physics, Department of Physics, Heinrich-Heine-Universität Düsseldorf

Frank Duzaar

Prof. Dr. Frank Duzaar

Publications

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Projects

Stability for doubly nonlinear parabolic equations (C07 intern)

Elliptische und parabolische Hindernis-Probleme mit irregulären Hindernissen

Prof. Dr. Frank Duzaar

Regularität von Lösungen quasilinearer subelliptischer Gleichungen mit Nichtstandard-Wachstum in der Heisenberg-Gruppe; Die singuläre Menge von Minima konvexer Variationsprobleme höherer Ordnung und Randregularität von Lösungen elliptischer Systeme

Prof. Dr. Frank Duzaar

Geometrische Variationsprobleme

Prof. Dr. Frank Duzaar

Curriculum Vitae

Scientific Vita