Diff. Geom, Math. Phys., PDE Seminar: François Hamel
- Date: 05/20/2014
- Time: 15:30
François Hamel, Université d'Aix-Marseille
University of British Columbia
Rearrangement inequalities and applications to elliptic eigenvalue problems
The talk will be concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. To each operator in a given domain, one can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.
Location: ESB 2012