Endpoint Morrey interior regularity of stable solutions to the p-Laplace equation

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Abstract

This paper establishes interior Morrey regularity for stable solutions of the p-Laplace equation $-\Delta_{p} u=h(u) \text { in } B_{1} \subset \mathbb{R}^{d}$, where h belongs to $C^{1}(\mathbb{R})$. The results cover the endpoint case left unresolved by Cabré et al. Moreover, for positive nonlinearities h, a global Morrey estimate was obtained for stable solutions of a Dirichlet problem on any smooth, bounded, strictly convex domain.

Keywords

stable solution / p-Laplacian / Morrey space / regularity

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