The paper claims invertible restrictions of the Laplace operator after removing a lower-dimensional manifold from a ball, a well-posed non-smooth Bitsadze-Samarskii problem, and a Krein trace formula for the resolvent difference.
Alexandrov, Combinatorial Topology, OGIZ, Moscow, 1947
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Singular perturbations of Laplace operator and their resolvents
The paper claims invertible restrictions of the Laplace operator after removing a lower-dimensional manifold from a ball, a well-posed non-smooth Bitsadze-Samarskii problem, and a Krein trace formula for the resolvent difference.