A spectral result for Hardy inequalities

Baptiste Devyver

A spectral result for Hardy inequalities

Spectral Theory 2014-01-09 v2 Analysis of PDEs

Authors: Baptiste Devyver

Abstract

Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$ ) and best constant $\alpha$ . We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$ . We apply this to several well-known Hardy inequalities: (improved) Hardy inequalities on a bounded convex domain with potential involving the distance to the boundary, and Hardy inequalities for minimal submanifolds of the Euclidean space.

Keywords

hardy inequalities hardy spaces spectral theory

Cite

@article{arxiv.1302.3039,
  title  = {A spectral result for Hardy inequalities},
  author = {Baptiste Devyver},
  journal= {arXiv preprint arXiv:1302.3039},
  year   = {2014}
}

Comments

To appear in J. Math Pures Appl. This version: extensive changes in the exposition, among which: a new introduction, and a new section about spectrum and Agmon metrics. New results and examples have also been added

A spectral result for Hardy inequalities

Abstract

Keywords

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