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

By Fritz Gesztesy, M. Mitrea. 2008

84 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ab83137bd874c88d92be2e12e69ddd14fd7d30e

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In Applied Mathematics

In Computational Theory and Mathematics

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Citations in the corpus

Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “Particular attention has been paid to the spectral properties of realizations with local and nonlocal Robin boundary conditions in [41, 106, 179, 180, 226, 325, 361, 413, 543, 628, 629, 665].”
Eventually and asymptotically positive semigroups on Banach lattices (2015, background): “Possibly the first paper studying this problem in a general setting was [30].”
Friedlander's eigenvalue inequalities and the Dirichlet-to-Neumann semigroup (2012, methodology): “An extension of Filonov’s ideas by Gesztesy and Mitrea [10] provides a comparison between generalized Robin and Dirichlet eigenvalues, while Safarov [24] showed how to describe all of this in a purely abstract setting involving only quadratic forms on Hilbert spaces.”
A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, background): “The following result has been proved in [57]:”