Gradient Estimate for Solutions of Second-Order Elliptic Equations

2021/11/22 by Maz'ya, Vladimir, McOwen, Robert
#35B45 (secondary) #35J15 (primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.11479

Abstract

We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x=0. In particular, we treat the case of solutions that are not Lipschitz continuous at x=0. We show that our estimate is sharp.

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