James Kennedy

University of Sydney (Austrialia)

Uniqueness in the Faber-Krahn inequality for Robin problems

We prove uniqueness in the Faber-Krahn inequality for the first eigenvalue of the Laplacian with Robin boundary conditions, asserting that amongst all sufficiently smooth domains of given volume, the ball is the unique minimiser for the first eigenvalue. The proof, which avoids the use of a symmetrisation of Schwarz, also works for Dirichlet boundary conditions. (Joint work with Daniel Daners)