A spectral result for Hardy inequalities

Baptiste Devyver

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arXiv · 1302.3039

A spectral result for Hardy inequalities

Baptiste Devyver

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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.

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Baptiste Devyver. 2013-02-13. A spectral result for Hardy inequalities. https://arxiv.org/abs/1302.3039

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