New extremal domains for the first eigenvalue of the Laplacian in flat toriReportar como inadecuado




New extremal domains for the first eigenvalue of the Laplacian in flat tori - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

Abstract : We prove the existence of nontrivial and noncompact extremal domains for the first eigenvalue of the Laplacian in some flat tori. Such domains can be extended by periodicity to nontrivial and noncompact domains in Euclidean spaces whose first eigenfunction of the Laplacian with 0 Dirichlet boundary condition has also constant Neumann data at the boundary, providing a couterexemple to a conjecture of Berestycki-Caffarelli-Nirenberg in dimension bigger or equal then 3. These domains are close to a straigh cylinder, they are invariant by rotation with respect to the vertical axe, and are not invariant by vertical translations.





Autor: Pieralberto Sicbaldi -

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



DESCARGAR PDF




Documentos relacionados