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Tuesday, November 03, 2020
11:00 AM - 11:50 AM
Online Event

Caltech/UCLA Joint Analysis Seminar

Two-phase free boundary problems and the Friedland-Hayman inequality
Thomas Beck, Mathematics Department, Fordham University,

The Friedland-Hayman inequality provides a lower bound on the first Dirichlet eigenvalues of complementary subsets of the sphere. In this talk, we will describe a variant of this inequality to geodesically convex subsets of the sphere with mixed Dirichlet-Neumann boundary conditions. Using this inequality, we prove an almost-monotonicity formula and Lipschitz continuity up to the boundary for the minimizer of a two-phase free boundary problem. This is joint work with David Jerison and Sarah Raynor.

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