Hardy inequality and Lp estimates for the torsion function

M. Van Den Berg; Tom Carroll

doi:10.1112/blms/bdp075

Hardy inequality and L^p estimates for the torsion function

M. Van Den Berg
, Tom Carroll

School of Mathematical Sciences

University of Bristol

Research output: Contribution to journal › Article › peer-review

Abstract

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^2p(D), if it is assumed that the Dirichlet Laplacian acting in L²(D) satisfies a strong Hardy inequality.

Original language	English
Pages (from-to)	980-986
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	41
Issue number	6
DOIs	https://doi.org/10.1112/blms/bdp075
Publication status	Published - Dec 2009

Access to Document

10.1112/blms/bdp075

Cite this

@article{5ddb0d4b7a19435aa470f4ff779e1961,

title = "Hardy inequality and Lp estimates for the torsion function",

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.",

author = "\{Van Den Berg\}, M. and Tom Carroll",

year = "2009",

month = dec,

doi = "10.1112/blms/bdp075",

language = "English",

volume = "41",

pages = "980--986",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "6",

}

TY - JOUR

T1 - Hardy inequality and Lp estimates for the torsion function

AU - Van Den Berg, M.

AU - Carroll, Tom

PY - 2009/12

Y1 - 2009/12

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/73149104411

U2 - 10.1112/blms/bdp075

DO - 10.1112/blms/bdp075

M3 - Article

AN - SCOPUS:73149104411

SN - 0024-6093

VL - 41

SP - 980

EP - 986

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 6

ER -

Hardy inequality and L^p estimates for the torsion function

Abstract

Access to Document

Other files and links

Fingerprint

Cite this