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Interaction of Boundary Singular Points in an Elliptic Boundary Value Problem
- Authors: Bogovskii A.M.1
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
- Issue: Vol 63, No 9 (2023)
- Pages: 1524-1530
- Section: Partial Differential Equations
- URL: https://ruspoj.com/0044-4669/article/view/664989
- DOI: https://doi.org/10.31857/S0044466923090041
- EDN: https://elibrary.ru/RJMDHQ
- ID: 664989
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Abstract
The paper continues the construction of the Lp-theory of elliptic Dirichlet and Neumann boundary value problems with discontinuous piecewise constant coefficients in divergent form for an unbounded domain R2 with a piecewise
smooth noncompact Lipschitz boundary and C1 smooth discontinuity lines of the coefficients. An earlier constructed Lp-theory is generalized to the case of different smallest eigenvalues corresponding to a finite and an infinite singular point, and the effect of their interaction is further studied in the class of functions with first derivatives from Lp( ) in the entire range of the exponent p (1, ).
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About the authors
A. M. Bogovskii
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Author for correspondence.
Email: abogovski@gmail.com
119991, Moscow, Russia
References
- Денисов В.Н., Боговский А.М. О взаимодействии граничных особых точек в задаче Дирихле для эллиптического уравнения с кусочно-постоянными коэффициентами в плоской области // Ж. вычисл. матем. и матем. физ. 2019. Т. 59. № 12. С. 2155–2174.
- Денисов В.Н., Боговский А.М. О взаимосвязи слабых решений эллиптических краевых задач Дирихле и Неймана для плоской односвязной области // Матем. заметки. 2020. Т. 107. № 1. С. 32–48.
- Brezis H. Functional analysis, Sobolev spaces and partial differential equations. Universitext. New York: Springer, 2011.
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