Local and global $C^{1,\beta }$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type

Abstract

We establish gradient Hölder continuity for solutions to quasilinear, uniformly elliptic equations, including $p$-Laplace and Orlicz-Laplace type operators. We revisit and improve upon the results existing in the literature, proving gradient regularity both in the interior and up to the boundary, under Dirichlet or Neumann boundary conditions.

arXiv commentExpanded the introduction with additional examples and references; fixed minor typos, added the Bernstein type inequality Proposition 7.3. Comments are welcome

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