 08232 Fritz Gesztesy and Marius Mitrea
 Nonlocal Robin Laplacians and some remarks on a paper by Filonov
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Dec 10, 08

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Abstract. The aim of this paper is twofold: First, we characterize an essentially optimal
class of boundary operators $\Theta$ which give rise to selfadjoint
Laplacians $\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with
(nonlocal and local)
Robintype 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.
 Files:
08232.tex