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

Gerassimos Barbatis; Pier Domenico Lamberti

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

Analysis of PDEs 2015-10-27 v2

Authors: Gerassimos Barbatis , Pier Domenico Lamberti

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.

Keywords

L^p Hardy inequality Hardy constant monotonicity continuity differentiability non-convex domain best constant

Cite

@article{arxiv.1509.09107,
  title  = {Monotonicity, continuity and differentiability results for the $L^p$ Hardy constant},
  author = {Gerassimos Barbatis and Pier Domenico Lamberti},
  journal= {arXiv preprint arXiv:1509.09107},
  year   = {2015}
}

Comments

12 pages; to appear in the Israel Journal of Mathematics

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