Affiliation:
1. Nikolskii Mathematical Institute, RUDN University, Miklukho-Maklaya Str. 6, 117198 Moscow, Russia
Abstract
We describe the Friedrichs extension of elliptic symmetric pseudodifferential operators on a closed smooth manifold with the domain consisting of functions vanishing on a given submanifold. In summary, the Friedrichs extension is an elliptic Sobolev problem defined in terms of boundary and coboundary operators, and the number of boundary and coboundary conditions in the problem depends on the order of the operator and the codimension of the submanifold. In this paper, the discreteness of the spectrum is proved, and singularities of eigenfunctions are described.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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