Isoperimetric inequalities and free discontinuity problems
Duration: 28 mins 52 secs
| Description: |
Bucur, D (Université de Savoie)
Wednesday 25 June 2014, 15:20-15:50 |
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| Created: | 2014-07-11 12:49 |
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| Collection: | Free Boundary Problems and Related Topics |
| Publisher: | Isaac Newton Institute |
| Copyright: | Bucur, D |
| Language: | eng (English) |
| Abstract: | The Faber-Krahn inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions was recently proved by D. Daners in the context of Lipschitz sets. This talk introduces a new approach to deal with this type of isoperimetric inequalities and is based on recent advances on the regularity theory for general free discontinuity problems, in particular on a new monotonicity formula jointly obtained with S. Luckhaus. As a consequence, we not only extend isoperimetric inequalities to arbitrary sets, but also obtain a range of new ones (joint work with A. Giacomini). |
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