Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions

Autor:	Aldeghi, Nausica, Rohleder, Jonathan
Rok vydání:	2022
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.05889 Zobrazit plný text záznamu View this record from Arxiv