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Isoperimetric inequalities and free discontinuity problems

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Free Boundary Problems and Related Topics

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).

This talk is part of the Isaac Newton Institute Seminar Series series.

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