University of Cambridge > Talks.cam > Partial Differential Equations seminar > Faber-Krahn inequalities for the principal eigenvalue of second order elliptic operators

Faber-Krahn inequalities for the principal eigenvalue of second order elliptic operators

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We show various optimization results for the principal eigenvalue of general uniformly elliptic second order operators under Dirichlet boundary condition in C2 bounded domains of Rn. In particular, we obtain a “Faber-Krahn” type inequality for these operators, which generalizes the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Laplacian. The proofs use a new rearrangement method. This is joint work with François Hamel and Nikolai Nadirashvili.

This talk is part of the Partial Differential Equations seminar series.

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