Universal potential estimates

Journal of Functional Analysis

Volumn 262, Issue 10, 2012, Pages 4205-4269

  Kuusi, Tuomo ^a   Mingione, Giuseppe ^b  

^a AALTO UNIVERSITY   (Finland)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

Potential estimates

Indexed keywords

EID: 84858795213     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2012.02.018     Document Type: Article

References (37)

1. Adams R.A., Fournier J.J.F. Sobolev Spaces. Pure Appl. Math. 2003, vol. 140. Elsevier, Academic Press, Amsterdam. second edition.
2. Boccardo L., Gallouët T. Nonlinear elliptic equations with right-hand side measures. Comm. Partial Differential Equations 1992, 17:641-655.
3. Byun S.S., Wang L. Parabolic equations with BMO nonlinearity in Reifenberg domains. J. Reine Angew. Math. (Crelles J.) 2008, 615:1-24.
4. 1,p estimates for elliptic equations in divergence form. Comm. Pure Appl. Math. 1998, 51:1-21.
5. DeVore R.A., Sharpley R.C. Maximal functions measuring smoothness. Mem. Amer. Math. Soc. 1984, 47(293).
6. 1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 1983, 7:827-850.
7. DiBenedetto E., Manfredi J.J. On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Amer. J. Math. 1993, 115:1107-1134.
8. Duzaar F., Mingione G. Gradient estimates via linear and nonlinear potentials. J. Funct. Anal. 2010, 259:2961-2998.
9. Duzaar F., Mingione G. Gradient continuity estimates. Calc. Var. Partial Differential Equations 2010, 39:379-418.
10. Duzaar F., Mingione G. Gradient estimates via nonlinear potentials. Amer. J. Math. 2011, 133:1093-1149.
11. Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Grundlehren Math. Wiss. 1977, vol. 224. Springer-Verlag, Berlin, New York.
12. Giusti E. Direct Methods in the Calculus of Variations 2003, World Scientific Publishing Co., Inc., River Edge, NJ.
13. Heinonen J., Kilpeläinen T., Martio O. Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Math. Monogr. 1993, Oxford Science Publ., The Claredon Press, Oxford Univ. Press, New York.
14. p-estimates for degenerated elliptic operators. Studia Math. 1983, 75:293-312.
15. Kilpeläinen T. Hölder continuity of solutions to quasilinear elliptic equations involving measures. Potential Anal. 1994, 3:265-272.
16. Kilpeläinen T., Malý J. The Wiener test and potential estimates for quasilinear elliptic equations. Acta Math. 1994, 172:137-161.
17. Kinnunen J., Zhou S. A local estimate for nonlinear equations with discontinuous coefficients. Comm. Partial Differential Equations 1999, 24:2043-2068.
18. Kristensen J., Mingione G. The singular set of minima of integral functionals. Arch. Ration. Mech. Anal. 2006, 180:331-398.
19. Kristensen J., Mingione G. Boundary regularity in variational problems. Arch. Ration. Mech. Anal. 2010, 198:369-455.
20. Kuusi T., Mingione G. Endpoint and intermediate potential estimates for nonlinear equations. Boll. Unione Mat. Ital. (9) 2011, 4:149-157.
21. Kuusi T., Mingione G. A surprising linear type estimate for nonlinear elliptic equations. C. R. Math. Acad. Sci. Paris 2011, 349:889-892.
22. T. Kuusi, G. Mingione, Linear potentials in nonlinear potential theory, preprint, 2011.
23. Lieberman G.M. Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 1988, 12:1203-1219.
24. Lieberman G.M. The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations. Comm. Partial Differential Equations 1991, 16:311-361.
25. Lieberman G.M. Sharp forms of estimates for subsolutions and supersolutions of quasilinear elliptic equations involving measures. Comm. Partial Differential Equations 1993, 18:1191-1212.
26. P. Lindqvist, Notes on the p-Laplace equation, Univ. Jyväskylä, Report 102, 2006.
27. J.J. Manfredi, Regularity of the gradient for a class of nonlinear possibly degenerate elliptic equations, PhD thesis, University of Washington, St. Louis.
28. Mingione G. The Calderón-Zygmund theory for elliptic problems with measure data. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2007, 6:195-261.
29. Mingione G. Gradient estimates below the duality exponent. Math. Ann. 2010, 346:571-627.
30. Mingione G. Nonlinear aspects of Calderón-Zygmund theory. Jahresber. Deutsch. Math.-Verein. 2010, 112:159-191.
31. Mingione G. Gradient potential estimates. J. Eur. Math. Soc. 2011, 13:459-486.
32. Mingione G. Nonlinear measure data problems. Milan J. Math. 2011, 79:429-496.
33. Phuc N.C., Verbitsky I.E. Quasilinear and Hessian equations of Lane-Emden type. Ann. of Math. (2) 2008, 168:859-914.
34. Phuc N.C., Verbitsky I.E. Singular quasilinear and Hessian equations and inequalities. J. Funct. Anal. 2009, 256:1875-1906.
35. Rakotoson J.M., Ziemer W.P. Local behavior of solutions of quasilinear elliptic equations with general structure. Trans. Amer. Math. Soc. 1990, 319:747-764.
36. Trudinger N.S., Wang X.J. On the weak continuity of elliptic operators and applications to potential theory. Amer. J. Math. 2002, 124:369-410.
37. Trudinger N.S., Wang X.J. Quasilinear elliptic equations with signed measure data. Discrete Contin. Dyn. Syst. 2009, 23:477-494.