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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