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arXiv · 2507.16402

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

Giuseppe Spadaro·Domenico Vuono
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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.

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Giuseppe Spadaro, Domenico Vuono. 2025-07-22. Second-order boundary estimates for solutions to a class of quasilinear elliptic equations. https://arxiv.org/abs/2507.16402

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