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An isoperimetric inequality for Gauss-like product measures
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...
| Published in: | Journal de Mathématiques Pures et Appliquées |
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| ISSN: | 00217824 |
| Published: |
2016
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa48744 |
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| 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 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. |
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| Keywords: |
relative isoperimetric inequalities, Polya–Szegö principle, degenerate elliptic equations |
| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
375 |
| End Page: |
391 |