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Séminaire de EDP - Physique Mathématique

On Dirichlet Laplace eigenfunctions in Lipschitz domains with small Lipschitz constant

Bilbao-Bordeaux-Toulouse Seminar: Eugenia Malinnikova

( Stanford and St-Petersbourg )

Salle de Conférences

le 11 mai 2021 à 15:00

We consider bounded domains in the Euclidean space with Lipschitz boundary and locally small Lipschitz constant. We proof the sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions in such domains. One of our tools is the analysis of the frequency function of a harmonic function vanishing on a part of the boundary. The talk is based on a joint work with A. Logunov, N. Nadirashvili, and F. Nazarov.