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An isoperimetric inequality for Gauss-like product measures

F. Brock, F. Chiacchio, A. Mercaldo, Friedemann Brock

Journal de Mathématiques Pures et Appliquées, Volume: 106, Issue: 2, Pages: 375 - 391

Swansea University Author: Friedemann Brock

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DOI (Published version): 10.1016/j.matpur.2016.02.014

Abstract

This paper deals with various questions related to the isoperimetric problem for a smooth positive measure in a domain of R^N. We find some necessary conditions on the density that render the intersection of half spaces with the domain a minimum in the isoperimetric problem. We then identify the uni...

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Published in: Journal de Mathématiques Pures et Appliquées
ISSN: 00217824
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa48744
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first_indexed 2019-02-11T11:58:03Z
last_indexed 2019-07-31T16:25:47Z
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spelling v2 48744 2019-02-07 An isoperimetric inequality for Gauss-like product measures d0a9ec2d7f8f2c8e27f5614ed1404a54 Friedemann Brock Friedemann Brock true false 2019-02-07 SMA This paper deals with various questions related to the isoperimetric problem for a smooth positive measure in a domain of R^N. We find some necessary conditions on the density that render the intersection of half spaces with the domain a minimum in the isoperimetric problem. We then identify the unique isoperimetric set for a class of factorized finite measures. These results are finally used in order to get sharp inequalities in weighted Sobolev spaces and a comparison result for solutions to boundary value problems for degenerate elliptic equations. Journal Article Journal de Mathématiques Pures et Appliquées 106 2 375 391 00217824 relative isoperimetric inequalities, Polya–Szegö principle, degenerate elliptic equations 2 8 2016 2016-08-02 10.1016/j.matpur.2016.02.014 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-06-23T18:09:34.3874662 2019-02-07T15:25:03.5601265 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics F. Brock 1 F. Chiacchio 2 A. Mercaldo 3 Friedemann Brock 4
title An isoperimetric inequality for Gauss-like product measures
spellingShingle An isoperimetric inequality for Gauss-like product measures
Friedemann Brock
title_short An isoperimetric inequality for Gauss-like product measures
title_full An isoperimetric inequality for Gauss-like product measures
title_fullStr An isoperimetric inequality for Gauss-like product measures
title_full_unstemmed An isoperimetric inequality for Gauss-like product measures
title_sort An isoperimetric inequality for Gauss-like product measures
author_id_str_mv d0a9ec2d7f8f2c8e27f5614ed1404a54
author_id_fullname_str_mv d0a9ec2d7f8f2c8e27f5614ed1404a54_***_Friedemann Brock
author Friedemann Brock
author2 F. Brock
F. Chiacchio
A. Mercaldo
Friedemann Brock
format Journal article
container_title Journal de Mathématiques Pures et Appliquées
container_volume 106
container_issue 2
container_start_page 375
publishDate 2016
institution Swansea University
issn 00217824
doi_str_mv 10.1016/j.matpur.2016.02.014
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 0
active_str 0
description This paper deals with various questions related to the isoperimetric problem for a smooth positive measure in a domain of R^N. We find some necessary conditions on the density that render the intersection of half spaces with the domain a minimum in the isoperimetric problem. We then identify the unique isoperimetric set for a class of factorized finite measures. These results are finally used in order to get sharp inequalities in weighted Sobolev spaces and a comparison result for solutions to boundary value problems for degenerate elliptic equations.
published_date 2016-08-02T18:09:28Z
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score 11.01628

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