Dorin Bucur

Quantitative isoperimetric inequalities for the Robin Laplacian

In this talk I will prove a quantitative form of the Faber-Krahn inequality for the first Robin-Laplacian eigenvalue. The key of the proof is based on the analysis of solutions of an auxiliary free discontinuity problem which, for a given set, produces a new one with almost the same Fraenkel asymmetry and lower eigenvalue. Further implications of this technique to other isoperimetric inequalities, like Saint Venant, will be discussed.