Local Lipschitz regularity for degenerate elliptic systems

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 27, Issue 6, 2010, Pages 1361-1396

  Duzaar, Frank ^a   Mingione, Giuseppe ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

NONLINEAR EQUATIONS;

A-PRIORI ESTIMATES; CRITICAL GROWTH; ELLIPTIC SYSTEM; GEOMETRIC ANALYSIS; GRADIENT BOUNDS; LIPSCHITZ; LIPSCHITZ REGULARITY; LORENTZ; NON-HOMOGENEOUS; NON-LINEAR; REGULAR SOLUTION; RIGHT-HAND SIDES; SPACE CHARACTERIZATION; TYPE SYSTEMS;

MATHEMATICAL OPERATORS;

EID: 78650029944     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2010.07.002     Document Type: Article

References (42)

1. A. Arkhipova Partial regularity up to the boundary of weak solutions of elliptic systems with nonlinearity q greater than two J. Math. Sci. (N. Y.) 115 2003 2735 2746
2. M.F. Betta, A. Mercaldo, F. Murat, and M.M. Porzio Existence of renormalized solutions to nonlinear elliptic equations with a lower-order term and right-hand side a measure J. Math. Pures Appl. (9) 82 2003 90 124
3. L. Boccardo, and T. Gallouët Nonlinear elliptic and parabolic equations involving measure data J. Funct. Anal. 87 1989 149 169
4. L. Boccardo, and T. Gallouët Nonlinear elliptic equations with right-hand side measures Comm. Partial Differential Equations 17 1992 641 655
5. A. Cianchi, V. Maz'ya, Global Lipschitz regularity for a class of quasilinear equations, preprint.
6. E. De Giorgi Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari Mem. Acad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (III) 125 3 1957 25 43
7. E. DiBenedetto C 1 + α local regularity of weak solutions of degenerate elliptic equations Nonlinear Anal. 7 1983 827 850
8. E. DiBenedetto Degenerate Parabolic Equations Universitext 1993 Springer-Verlag New York
9. G. Dolzmann, N. Hungerbühler, and S. Müller The p-harmonic system with measure-valued right-hand side Ann. Inst. H. Poincare Anal. Non Lineaire 14 1997 353 364
10. F. Duzaar, J. Kristensen, and G. Mingione The existence of regular boundary points for non-linear elliptic systems J. Reine Angew. Math. (Crelles J.) 602 2007 17 58
11. F. Duzaar, and G. Mingione Gradient estimates in non-linear potential theory Rend. Lincei - Mat. Appl. 20 2009 179 190
12. F. Duzaar, G. Mingione, Gradient estimates via non-linear potentials, Amer. J. Math., in press.
13. F. Duzaar, G. Mingione, Gradient continuity estimates, Calc. Var. Partial Differential Equations, doi:10.1007/s00526-010-0314-6.
14. L. Esposito, F. Leonetti, and G. Mingione Regularity results for minimizers of irregular integrals with (p, q ) growth Forum Math. 14 2002 245 272
15. E. Giusti Direct Methods in the Calculus of Variations 2003 World Scientific Publishing Co., Inc. River Edge, NJ
16. C. Hamburger Regularity of differential forms minimizing degenerate elliptic functionals J. Reine Angew. Math. (Crelles J.) 431 1992 7 64
17. F. Hélein Harmonic Maps, Conservation Laws and Moving Frames second ed. Cambridge Tracts in Math. vol. 150 2002 Cambridge University Press Cambridge
18. F. Hélein, and J. Wood Harmonic maps Handbook of Global Analysis vol. 1213 2008 Elsevier Sci. B.V. Amsterdam 417 491
19. S. Hildebrandt, and K.O. Widman Some regularity results for quasilinear elliptic systems of second order Math. Z. 142 1975 67 86
20. L.I. Hunt On L (p, q ) spaces L'Einsegnement Math. 12 1966 249 276
21. T. Iwaniec p-Harmonic tensors and quasiregular mappings Ann. of Math. (2) 136 1992 589 624
22. T. Iwaniec, and C. Sbordone Weak minima of variational integrals J. Reine Angew. Math. (Crelles J.) 454 1994 143 161
23. T. Kilpeläinen, and J. Malý The Wiener test and potential estimates for quasilinear elliptic equations Acta Math. 172 1994 137 161
24. J. Kristensen, and C. Melcher Regularity in oscillatory nonlinear elliptic systems Math. Z. 260 2008 813 847
25. T. Kuusi, G. Mingione, Potential estimates and gradient boundedness for nonlinear parabolic systems, preprint, 2010.
26. J. Leray, and J.-L. Lions Quelques résultats de Višik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder Bull. Soc. Math. France 93 1965 97 107
27. G.M. Lieberman Sharp forms of estimates for subsolutions and supersolutions of quasilinear elliptic equations involving measures Comm. Partial Differential Equations 18 1993 1191 1212
28. J.L. Lions Quelques méthodes de résolution des problèmes aux limites non linéaires 1969 Dunod/Gauthier-Villars Paris
29. V. Maz'ya The boundedness of the first derivatives of the solution of the Dirichlet problem in a region with smooth nonregular boundary Vestnik Leningrad. Univ. 24 1969 72 79 (in Russian)
30. V. Maz'ya Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain C. R. Acad. Sci. Paris Ser. I 347 2008 517 520
31. G. Mingione Regularity of minima: an invitation to the dark side of the calculus of variations Appl. Math. 51 2006 355 425
32. G. Mingione The Calderón-Zygmund theory for elliptic problems with measure data Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 2007 195 261
33. G. Mingione Gradient estimates below the duality exponent Math. Ann. 346 2010 571 627
34. G. Mingione, Gradient potential estimates, J. Europ. Math. Soc., in press.
35. T. Rivière Conservation laws for conformally invariant variational problems Invent. Math. 168 2007 1 22
36. T. Rivière, Integrability by compensation in the analysis of conformally invariant problems, lecture notes.
37. T. Rivière, Sub-criticality of Schroedinger systems with antisymmetric potentials, preprint, 2009.
38. E.M. Stein, and G. Weiss Introduction to Fourier Analysis on Euclidean Spaces Princeton Math. Ser. vol. 32 1971 Princeton University Press Princeton, NJ
39. N.S. Trudinger, and X.J. Wang On the weak continuity of elliptic operators and applications to potential theory Amer. J. Math. 124 2002 369 410
40. N.S. Trudinger, and X.J. Wang Quasilinear elliptic equations with signed measure data Discrete Contin. Dyn. Syst. A 23 2009 477 494
41. K. Uhlenbeck Regularity for a class of non-linear elliptic systems Acta Math. 138 1977 219 240
42. N.N. Ural'tseva Degenerate quasilinear elliptic systems Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 7 1968 184 222