HARDY and RELLICH INEQUALITIES on the COMPLEMENT of CONVEX SETS

Derek W. Robinson

doi:10.1017/S1446788718000356

HARDY and RELLICH INEQUALITIES on the COMPLEMENT of CONVEX SETS

Derek W. Robinson^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We establish existence of weighted Hardy and Rellich inequalities on the spaces, where with a closed convex subset of . Let denote the boundary of and the Euclidean distance to . We consider weighting functions with and . Then the Hardy inequalities take the form (Formula Present) and the Rellich inequalities are given by with . The constants depend on the weighting parameters and the Hausdorff dimension of the boundary. We compute the optimal constants in a broad range of situations.

Original language	English
Pages (from-to)	98-119
Number of pages	22
Journal	Journal of the Australian Mathematical Society
Volume	108
Issue number	1
DOIs	https://doi.org/10.1017/S1446788718000356
Publication status	Published - 1 Feb 2020

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title = "HARDY and RELLICH INEQUALITIES on the COMPLEMENT of CONVEX SETS",

abstract = "We establish existence of weighted Hardy and Rellich inequalities on the spaces, where with a closed convex subset of . Let denote the boundary of and the Euclidean distance to . We consider weighting functions with and . Then the Hardy inequalities take the form (Formula Present) and the Rellich inequalities are given by with . The constants depend on the weighting parameters and the Hausdorff dimension of the boundary. We compute the optimal constants in a broad range of situations.",

keywords = "Hardy inequality, Rellich inequality",

author = "Robinson, \{Derek W.\}",

note = "Publisher Copyright: {\textcopyright} 2018 Australian Mathematical Publishing Association Inc.",

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AU - Robinson, Derek W.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We establish existence of weighted Hardy and Rellich inequalities on the spaces, where with a closed convex subset of . Let denote the boundary of and the Euclidean distance to . We consider weighting functions with and . Then the Hardy inequalities take the form (Formula Present) and the Rellich inequalities are given by with . The constants depend on the weighting parameters and the Hausdorff dimension of the boundary. We compute the optimal constants in a broad range of situations.

AB - We establish existence of weighted Hardy and Rellich inequalities on the spaces, where with a closed convex subset of . Let denote the boundary of and the Euclidean distance to . We consider weighting functions with and . Then the Hardy inequalities take the form (Formula Present) and the Rellich inequalities are given by with . The constants depend on the weighting parameters and the Hausdorff dimension of the boundary. We compute the optimal constants in a broad range of situations.

KW - Hardy inequality

KW - Rellich inequality

UR - https://www.scopus.com/pages/publications/85077974673

U2 - 10.1017/S1446788718000356

DO - 10.1017/S1446788718000356

M3 - Article

SN - 1446-7887

VL - 108

SP - 98

EP - 119

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 1

ER -

HARDY and RELLICH INEQUALITIES on the COMPLEMENT of CONVEX SETS

Abstract

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