On the Uniqueness of the Recovery of the Domain of the Perturbed Laplace Operator

2022

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DOI 10.1134/s1995080222090116
Data confidence 70 medium
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Abstract

Abstract The paper gives a correct definition of the formal Laplace operator with delta-shaped perturbation. To define the area of use, the limiting potentials of simple and double layers are used. It is proved that from a set of spectra of some reference operators it is possible to unambiguously reconstruct the boundary densities of the potentials and the double layer. Moreover, one of the reference operators coincides with the original Laplace operator with delta-like perturbation.