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1 LM-Orsay - Laboratoire de Mathématiques d-Orsay

Abstract : In this paper, we determine, in the case of the Laplacian on the flat two-dimensional torus R-Z 2 , all the eigenvalues having an eigenfunction which satisfies Courant-s theorem with equality Courant-sharp situation. Following the strategy o A. Pleijel 1956, the proof is a combination of a lower bound a la Weyl of the counting function, with an explicit remainder term, and of a Faber–Krahn inequality for domains on the torus deduced as in Bérard-Meyer from an isoperimetric inequality, with an explicit upper bound on the area.

Keywords : Courant theorem torus Pleijel theorem Nodal domains





Autor: Corentin Léna -

Fuente: https://hal.archives-ouvertes.fr/



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