Harnack's inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients

DOI10.1016/j.na.2015.05.029zbMath1323.35045arXiv1411.6976OpenAlexW2963221819MaRDI QIDQ494189

Richard L. Wheeden, Scott Rodney, Dario Daniele Monticelli

Publication date: 31 August 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6976

zbMATH Keywords

regularityweak solutionsquasilinear equationsHölder continuityHarnack's inequalitydegenerate quadratic formsMoser methoddegenerate elliptic partial differential equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Weak solutions to PDEs (35D30)

Related Items (12)

Weighted \(W^{1, p}\) estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable ⋮ Harnack's inequality and applications of quasilinear degenerate elliptic equations with rough and singular coefficients ⋮ Existence of weak solutions to degenerate \(p\)-Laplacian equations and integral formulas ⋮ Matrix weights and regularity for degenerate elliptic equations ⋮ Sharp pointwise estimates for weighted critical \(p\)-Laplace equations ⋮ Boundedness and regularity of solutions of degenerate elliptic partial differential equations ⋮ Two weight bump conditions for matrix weights ⋮ Global Sobolev inequalities and degenerate \(p\)-Laplacian equations ⋮ Weighted Calderón-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations ⋮ Embedding and compact embedding for weighted and abstract Sobolev spaces ⋮ Poincare Inequalities and Neumann Problems for the p-Laplacian ⋮ Weighted-W^{1,p} estimates for weak solutions of degenerate and singular elliptic equations

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