Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities

Details Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities

2008-12-10

arxiv.org/abs/0812.2047v4

Mathematics

Spectral Theory

23 pages, added Remark 5.4

Scientific paper

The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators $\Theta$ which give rise to self-adjoint Laplacians $-\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with (nonlocal and local) Robin-type boundary conditions on bounded Lipschitz domains $\Omega\subset\bbR^n$, $n\in\bbN$, $n\geq 2$. Second, we extend Friedlander's inequalities between Neumann and Dirichlet Laplacian eigenvalues to those between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with bounded Lipschitz domains $\Omega$, following an approach introduced by Filonov for this type of problems.

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