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 a constant is in general not explicitly known.
Monotonicity, continuity and differentiability results for the Lp Hardy constant
LAMBERTI, PIER DOMENICO
2016
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 a constant is in general not explicitly known.
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