Refined Rellich boundary inequalities for the derivatives of a harmonic function

2022/05/10 by Agrawal, Siddhant, Alazard, Thomas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.04756

Abstract

The classical Rellich inequalities imply that the L²-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp L^p-estimate for 1

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