The Correct Definition of Second-Order Elliptic Operators with Point Interactions and their Resolvents

2020

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DOI 10.3103/s1055134420030013
Data confidence 70 medium
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Abstract

A finite number of interior points is removed from an open bounded simply connected domain with smooth boundary in a multidimensional space. In the resulting domain, we consider correctly solvable boundary value problems for a second-order elliptic operator with variable coefficients. The domain of such problems may contain functions that have a singularity of the type of the fundamental solution and its partial derivatives.