On Yau’s conjecture for the Dirichlet Laplacian in C^1 domains

Prof Eugenia Malinnikova (Stanford)

12-Feb-2021, 15:00-16:00 (3 years ago)

Abstract: Let D be a bounded domain in R^n with C^1 boundary and let u be a Dirichlet Laplace eigenfunction in D with eigenvalue λ. We show that the (n − 1)-dimensional Hausdorff measure of the zero set of u does not exceed C√λ. The opposite estimate follows from the work of Donnelly and Fefferman. The talk is based on a joint work with A. Logunov, N. Nadirashvili, and F. Nazarov..

analysis of PDEs

Audience: researchers in the topic


Open PDE and analysis seminar and lectures

Organizers: Benoit Pausader*, Clement Mouhot*, Ivan Moyano, Thomas Alazard, Nicolas Burq*, Marjolaine Puel
*contact for this listing

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