Singular perturbations of Laplace operator and their resolvents

2019

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DOI 10.1080/17476933.2019.1655551
Data confidence 70 medium
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Abstract

An inner closed (without boundary) smooth manifold of a lower dimension is cut from a multidimensional ball. In this region, invertible restrictions of the Laplace operator are well defined. In particular, the well-posed non-smooth Bitsadze-Samarskiĭ problem for the Laplace equation is defined. Moreover, we obtain M.G. Krein's formula for the trace of the difference of resolvents of the studied operators. We prove assertions on the spectrum of the non-smooth Bitsadze-Samarskiĭ problem.