Event № 189
Broadly speaking, an eigenvalue appearing in the boundary conditions of an elliptic operator is an eigenvalue of Steklov-type.
In this talk we shall discuss a few variants of the classical second order Steklov problem. In particular, we shall formulate the naturalfourth order Steklov problem which involves the biharmonic operator, providing a physical justification.
Shape optimization problems will be addressed and an isoperimetric inequality for the first eigenvalue of the above mentionedbiharmonic Steklov problem will be presented.We shall also point out that a class of Steklov-type problems could be viewed as a class of critical Neumann-type problems arisingin boundary mass concentration phenomena.
This talk is based on joint works with Davide Buoso and Luigi Provenzano.