First and second variation of domain functionals and applications to problems with Robin boundary conditions.
Seminar Room 2, Newton Institute Gatehouse
We discuss the first and second domain variation for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions. A characterization of optimal domains is obtained. Special attention is given to perturbations of the ball where the first variation vanishes. The sign of the second variation depends on the eigenvalues of a Steklov problem. A stability result for nearly circular domains follows as a byproduct. The talk is based on a project in collaboration with Alfred Wagner.