Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
Analysis of PDEs
2025-07-23 v1
Abstract
We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required.
Keywords
Cite
@article{arxiv.2507.16402,
title = {Second-order boundary estimates for solutions to a class of quasilinear elliptic equations},
author = {Giuseppe Spadaro and Domenico Vuono},
journal= {arXiv preprint arXiv:2507.16402},
year = {2025}
}