Hardy inequalities for p-Laplacians with Robin boundary conditions

Tomas Ekholm; Hynek Kovarik; Ari Laptev

Hardy inequalities for p-Laplacians with Robin boundary conditions

Analysis of PDEs 2014-07-22 v1 Spectral Theory

Authors: Tomas Ekholm , Hynek Kovarik , Ari Laptev

Abstract

In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals $((p-1)/p)^p$ whenever Dirichlet boundary conditions are imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.

Keywords

Hardy inequality p-Laplacian Robin boundary conditions convex domains best constant Dirichlet boundary conditions

Cite

@article{arxiv.1407.5518,
  title  = {Hardy inequalities for p-Laplacians with Robin boundary conditions},
  author = {Tomas Ekholm and Hynek Kovarik and Ari Laptev},
  journal= {arXiv preprint arXiv:1407.5518},
  year   = {2014}
}

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