Hardy inequality and L p estimates for the torsion function
M. van den Berg, Tom Carroll · Bulletin of the London Mathematical Society · 2009
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.