Boundary regularity for quasilinear elliptic equations with general Dirichlet boundary data

Abstract

We study global regularity for solutions of quasilinear elliptic equations of the form $÷\A(x,u,\nabla u) = ÷\F $ in rough domains $\Omega$ in ${\mathbb{R}}^n$ with nonhomogeneous Dirichlet boundary condition. The vector field $\A$ is assumed to be continuous in $u$, and its growth in $\nabla u$ is like that of the $p$-Laplace operator. We establish global gradient estimates in weighted Morrey spaces for weak solutions $u$ to the equation under the Reifenberg flat condition for $\Omega$, a small BMO condition in $x$ for $\A$, and an optimal condition for the Dirichlet boundary data.

arXiv admin note: text overlap with arXiv:1810.12496

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