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, 2021, Volume 191, Pages 105–114
DOI: https://doi.org/10.36535/0233-6723-2021-191-105-114 (Mi into769) 		 
Investigation of singularly perturbed and irregularly degenerate elliptic problems

I. S. Lomov

Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2021-191-105-114
Abstract: Using two elliptic problems as examples, we show that the method of regularization of singular perturbations developed for constructing regularized asymptotic solutions of singularly perturbed equations can be successfully applied to constructing solutions of irregularly degenerate elliptic problems.
Keywords: singular perturbation, spectrum, degenerate elliptic equation, small parameter, asymptotic series.
English version:
Journal of Mathematical Sciences (New York), 2025, Volume 288, Issue 6, Pages 770–779
DOI: https://doi.org/10.1007/s10958-025-07766-5
Document Type: Article
UDC: 517.956.226
MSC: 35J75
Language: Russian
Citation: I. S. Lomov, “Investigation of singularly perturbed and irregularly degenerate elliptic problems”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 191, VINITI, Moscow, 2021, 105–114; J. Math. Sci. (N. Y.), 288:6 (2025), 770–779
Citation in format AMSBIB
\Bibitem{Lom21}
\by I.~S.~Lomov
\paper Investigation of singularly perturbed and irregularly degenerate elliptic problems
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 191
\pages 105--114
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into769}
\crossref{https://doi.org/10.36535/0233-6723-2021-191-105-114}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2025
\vol 288
\issue 6
\pages 770--779
\crossref{https://doi.org/10.1007/s10958-025-07766-5}
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