Hardy inequality and L p estimates for the torsion function

2009/09/03 by M. van den Berg, Tom Carroll · 5 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #Advanced Harmonic Analysis Research

paper · doi:10.1112/blms/bdp075

Abstract

It is shown that the torsion function for an open set D in Euclidean space ℝm is in L∞(D) if and only if the spectrum of the Dirichlet Laplacian in D is bounded away from 0. For 1 ⩽ p ⩽ ∞, it is shown that the torsion function for D is in Lp(D) precisely when the distance to the boundary function is in L2p(D), if it is assumed that the Dirichlet Laplacian acting in L2(D) satisfies a strong Hardy inequality.

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