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Symmetry and asymmetry of minimizers of a class of noncoercive functionals
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...
| Published in: | Advances in Calculus of Variations |
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| ISSN: | 1864-8258 1864-8266 |
| Published: |
Walter de Gruyter GmbH
2020
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa48732 |
| 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 from this axis. In the two-dimensional case, we show a symmetry breaking. |
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| Keywords: |
Foliated Schwarz symmetry, Euler equation, symmetry breaking |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
15 |
| End Page: |
32 |