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Some isoperimetric inequalities on RN with respect to weights | x | α
Journal of Mathematical Analysis and Applications, Volume: 451, Issue: 1, Pages: 280 - 318
Swansea University Author: Friedemann Brock
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DOI (Published version): 10.1016/j.jmaa.2017.01.085
Abstract
We solve a class of isoperimetric problems on R^N with respect to weights that are powers of the distance to the origin. In turn, we establish radiality of optimizers in some Caffarelli–Kohn–Nirenberg inequalities, and we obtain sharp bounds for eigenvalues of some nonlinear problems.
| Published in: | Journal of Mathematical Analysis and Applications |
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| ISSN: | 0022-247X |
| Published: |
Elsevier BV
2017
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa48740 |
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| Abstract: |
We solve a class of isoperimetric problems on R^N with respect to weights that are powers of the distance to the origin. In turn, we establish radiality of optimizers in some Caffarelli–Kohn–Nirenberg inequalities, and we obtain sharp bounds for eigenvalues of some nonlinear problems. |
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| Keywords: |
isoperimetric inequality, weighted rearrangement, norm inequality, elliptic boundary value problem, eigenvalue problem |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
280 |
| End Page: |
318 |