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Hardy inequality and L p estimates for the torsion function
Author(s) -
van den Berg M.,
Carroll Tom
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp075
Subject(s) - mathematics , torsion (gastropod) , laplace operator , bounded function , euclidean space , open set , mathematical analysis , combinatorics , pure mathematics , medicine , surgery
It is shown that the torsion function for an open set D in Euclidean space ℝ m 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 L p ( D ) precisely when the distance to the boundary function is in L 2 p ( D ), if it is assumed that the Dirichlet Laplacian acting in L 2 ( D ) satisfies a strong Hardy inequality.
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