A note on gradient estimates for p-Laplacian equations

2023/02/23 by Guarnotta, Umberto, Marano, Salvatore A.
#35D30 #35D35 #35J15 #35J47 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.11927

Abstract

The aim of this short paper is to show that some assumptions in [10] can be relaxed and even dropped when looking for weak solutions instead of strong ones. This improvement is a consequence of two results concerning gradient terms: an L^∞ estimate, which exploits nonlinear potential theory, and a compactness result, based on the classical Riesz-Fréchet-Kolmogorov theorem.

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