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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 173, Pages 65–71
DOI: https://doi.org/10.36535/0233-6723-2019-173-65-71 (Mi into557) 		 
Holomorphic regularization of boundary-value problems for Tikhonov systems

V. I. Kachalov

National Research University "Moscow Power Engineering Institute"
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DOI: https://doi.org/10.36535/0233-6723-2019-173-65-71
Abstract: One of directions in the development of Lomov's regularization method is the approach related to holomorphic regularization of singularly perturbed problems, which allows one to construct solutions to such problems in the form of series in powers of a small parameter converging in the usual sense. For boundary-value problems, the problem of pseudoholomorphic continuation of solutions is very urgent. In this paper, we examine a boundary-value problem for a Tikhonov system and give conditions for the existence of its pseudoholomorphic solution.
Keywords: holomorphic regularization, pseudoholomorphic solution, Tikhonov system, pseudoholomorphic continuation, essentially singular manifold.
Document Type: Article
UDC: 517.925
MSC: 34E05, 34E20
Language: Russian
Citation: V. I. Kachalov, “Holomorphic regularization of boundary-value problems for Tikhonov systems”, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 173, VINITI, Moscow, 2019, 65–71
Citation in format AMSBIB
\Bibitem{Kac19}
\by V.~I.~Kachalov
\paper Holomorphic regularization of boundary-value problems for Tikhonov systems
\inbook Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 173
\pages 65--71
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into557}
\crossref{https://doi.org/10.36535/0233-6723-2019-173-65-71}
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