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Caltech/UCLA Joint Analysis Seminar

Tuesday, November 3, 2020
11:00am to 11:50am
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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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.