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Symmetry and asymmetry of minimizers of a class of noncoercive functionals

Friedemann Brock, Gisella Croce, Olivier Guibé, Anna Mercaldo

Advances in Calculus of Variations, Volume: 13, Issue: 1, Pages: 15 - 32

Swansea University Author: Friedemann Brock

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DOI (Published version): 10.1515/acv-2017-0005

Abstract

We prove symmetry results for minimizers of a noncoercive functional defined on theclass of Sobolev functions with zero mean value. The minimizers are foliated Schwarz symmetric,i.e., they are axially symmetric with respect to an axis passing through the origin and nonincreasingin the polar angle fr...

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Published in: Advances in Calculus of Variations
ISSN: 1864-8258 1864-8266
Published: Walter de Gruyter GmbH 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa48732
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first_indexed 2019-02-11T11:58:02Z
last_indexed 2019-07-31T16:25:45Z
id cronfa48732
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spelling v2 48732 2019-02-07 Symmetry and asymmetry of minimizers of a class of noncoercive functionals d0a9ec2d7f8f2c8e27f5614ed1404a54 Friedemann Brock Friedemann Brock true false 2019-02-07 SMA We prove symmetry results for minimizers of a noncoercive functional defined on theclass of Sobolev functions with zero mean value. The minimizers are foliated Schwarz symmetric,i.e., they are axially symmetric with respect to an axis passing through the origin and nonincreasingin the polar angle from this axis. In the two-dimensional case, we show a symmetry breaking. Journal Article Advances in Calculus of Variations 13 1 15 32 Walter de Gruyter GmbH 1864-8258 1864-8266 Foliated Schwarz symmetry, Euler equation, symmetry breaking 31 12 2020 2020-12-31 10.1515/acv-2017-0005 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-06-23T18:09:29.6299867 2019-02-07T14:36:57.5589885 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Friedemann Brock 1 Gisella Croce 2 Olivier Guibé 3 Anna Mercaldo 4
title Symmetry and asymmetry of minimizers of a class of noncoercive functionals
spellingShingle Symmetry and asymmetry of minimizers of a class of noncoercive functionals
Friedemann Brock
title_short Symmetry and asymmetry of minimizers of a class of noncoercive functionals
title_full Symmetry and asymmetry of minimizers of a class of noncoercive functionals
title_fullStr Symmetry and asymmetry of minimizers of a class of noncoercive functionals
title_full_unstemmed Symmetry and asymmetry of minimizers of a class of noncoercive functionals
title_sort Symmetry and asymmetry of minimizers of a class of noncoercive functionals
author_id_str_mv d0a9ec2d7f8f2c8e27f5614ed1404a54
author_id_fullname_str_mv d0a9ec2d7f8f2c8e27f5614ed1404a54_***_Friedemann Brock
author Friedemann Brock
author2 Friedemann Brock
Gisella Croce
Olivier Guibé
Anna Mercaldo
format Journal article
container_title Advances in Calculus of Variations
container_volume 13
container_issue 1
container_start_page 15
publishDate 2020
institution Swansea University
issn 1864-8258
1864-8266
doi_str_mv 10.1515/acv-2017-0005
publisher Walter de Gruyter GmbH
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 We prove symmetry results for minimizers of a noncoercive functional defined on theclass of Sobolev functions with zero mean value. The minimizers are foliated Schwarz symmetric,i.e., they are axially symmetric with respect to an axis passing through the origin and nonincreasingin the polar angle from this axis. In the two-dimensional case, we show a symmetry breaking.
published_date 2020-12-31T18:09:23Z
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score 11.01628

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