Il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terrà mercoledì 30 ottobre 2024 alle ore 15.00, nella Sala Professori 1° Livello. Di seguito, riportiamo i nomi dei due speaker e gli abstract dei loro talk.

Antonio Celentano: Shape optimization and overdetermined problems
Abstract: In this talk, we emphasize the connection between shape optimization and overdetermination. Overdeterminated problems usually arise from the shape optimization context by imposing the optimality condition computed via domain derivative. We present a Serrin-type result for an elliptic system of equations, overdetermined with both Dirichlet and generalized Neumann conditions. With this tool, we characterize the critical shapes of some domain functionals under volume constraints.
The talk is based on the paper “On a Serrin-type overdetermined problem” (MJM 2024) in collaboration with C. Nitsch and C. Trombetti.

Emanuele Cristoforoni:  A spectral inequality for the Robin-Laplacian on the sphere with negative boundary parameter
Abstract: We study the problem of maximizing the first eigenvalue of the Robin-Laplacian, with negative boundary parameter, among the convex subsets of the n-sphere with fixed perimeter. In particular, we show that convex balls are maximizers.