Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 168, Pages 26–32
DOI: https://doi.org/10.36535/0233-6723-2019-168-26-32 (Mi into498) 		 
On certain operator families

V. B. Vasil'ev (Vasilyev)

National Research University "Belgorod State University"
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DOI: https://doi.org/10.36535/0233-6723-2019-168-26-32
Abstract: In this paper, we propose an abstract scheme for the study of special operators and apply this scheme to examining elliptic pseudodifferential operators and related boundary-value problems on manifolds with nonsmooth boundaries. In particular, we consider cases where boundaries may contain conical points, edges of various dimensions, and even peak points. Using the constructions proposed, we present well-posed formulations of boundary-value problems for elliptic pseudo-differential equations on manifolds discussed in Sobolev–Slobodecky spaces.
Keywords: local-type operator, operator symbol, ellipticity, Fredholm property, index, pseudodifferential operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.7311.2017/8.9
This work was supported by the Ministry of Education and Science of the Russian Federation (project No. 1.7311.2017/8.9).
Document Type: Article
UDC: 517.983
MSC: 35S05, 47B37
Language: Russian
Citation: V. B. Vasil'ev (Vasilyev), “On certain operator families”, Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 168, VINITI, Moscow, 2019, 26–32
Citation in format AMSBIB
\Bibitem{Vas19}
\by V.~B.~Vasil'ev~(Vasilyev)
\paper On certain operator families
\inbook Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25--28, 2018. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 168
\pages 26--32
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into498}
\crossref{https://doi.org/10.36535/0233-6723-2019-168-26-32}
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