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Brief communications

On Sobolev problems associated with actions of Lie groups

D. A. Loshchenova

Chair of Applied Mathematics, Peoples' Friendship University of Russia, 6 Miklukho-Maklaya str., Moscow, 117198 Russia

Abstract: We consider Sobolev problems with nonlocal boundary conditions associated with an action of a compact Lie group. We give a natural notion of ellipticity of such problems and obtain the corresponding finiteness theorem and give the index formula.

Keywords: elliptic operators, Sobolev problems, fixed points of Lie group action, operators concentrated in a point.

UDC: 517.9

Presented by the member of Editorial Board: V. G. Zvyagin
Received: 13.01.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:9, 57–61

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