Global Hoelder continuity of solutions to quasilinear equations with Morrey data

Abstract

We deal with general quasilinear divergence-form coercive operators whose prototype is the $m$-Laplacean operator. The nonlinear terms are given by Carathéodory functions and satisfy controlled growth structure conditions with data belonging to suitable Morrey spaces. The fairly non-regular boundary of the underlying domain is supposed to satisfy a capacity density condition which allows domains with exterior corkscrew property. We prove global boundedness and Hoelder continuity up to the boundary for the weak solutions of such equations, generalizing this way the classical $L^p$-result of Ladyzhenskaya and Ural'tseva to the settings of the Morrey spaces.

to appear in "Communications in Contemporary Mathematics"

References in corpus (1)

• Weighted $L^p$-estimates for elliptic equations with measurable coefficients in nonsmooth domains

Cited by in corpus (3)

• Boundedness of the solutions of a kind of nonlinear parabolic systems
• Concavity and perturbed concavity for $p$-Laplace equations
• Global Hölder solvability of second order elliptic equations with locally integrable lower-order coefficients