3 may 2001

Abstract.

Edouard Oudet (Universite' de Strasbourg + Universita' di Pisa) ``Optimization of the second Dirichlet's eigenvalue under volume and convexity constraints.'' Dipartimento di Matematica - Sala dei Seminari

Giovedi' 3 Maggio 2001 - Ore 18.00 ABSTRACT: After a short introduction on classical eigenvalues problems we will study a question proposed by Troesh in 1973: does the stadium (the convex hull of two tangent balls of same radius) minimize the second Dirichlet's eigenvalue among convex domains with prescribed volume? After the theorical study of the optimal shape we will answer to Troesh's question and draw other consequences of the demonstration. In a third time we will present a numerical description of the optimal shape.