Monotonicity, continuity and differentiability results for the L^p Hardy constant

2015/09/30 by Barbatis, Gerassimos, Lamberti, Pier Domenico
#26D15 #35P15 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.09107

Abstract

We consider the L^p Hardy inequality involving the distance to the boundary for a domain in the n-dimensional Euclidean space. We study the dependence on p of the corresponding best constant and we prove monotonicity, continuity and differentiability results. The focus is on non-convex domains in which case such constant is in general not explicitly known.

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