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)
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