A geometric approximation of non-local interface and boundary conditions
A geometric approximation of non-local interface and boundary conditions
We analyze an approximation of a Laplacian subject to non-local interface conditions of a $δ'$-type by Neumann Laplacians on a family of Riemannian manifolds with a sieve-like structure. We establish a (kind of) resolvent convergence for such operators, which in turn implies the convergence of spectra and eigenspaces, and demonstrate convergence of the corresponding semigroups. Moreover, we provide an explicit example of a manifold allowing to realize any prescribed integral kernel appearing in that interface conditions. Finally, we extend the discussion to similar approximations for the Laplacian with non-local Robin-type boundary conditions.
Pavel Exner、Andrii Khrabustovskyi
数学
Pavel Exner,Andrii Khrabustovskyi.A geometric approximation of non-local interface and boundary conditions[EB/OL].(2025-06-23)[2025-07-23].https://arxiv.org/abs/2505.19016.点此复制
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