On the Interaction of Boundary Singular Points in the Dirichlet Problem for an Elliptic Equation with Piecewise Constant Coefficients in a Plane Domain
- Authors: Bogovskii A.M.1, Denisov V.N.1
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
- Issue: Vol 59, No 12 (2019)
- Pages: 2145-2163
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/180950
- DOI: https://doi.org/10.1134/S0965542519110046
- ID: 180950
Cite item
Abstract
For an elliptic equation in divergent form with a discontinuous scalar piecewise constant coefficient in an unbounded domain \(\Omega \subset {{\mathbb{R}}^{2}}\) with a piecewise smooth noncompact boundary and smooth discontinuity lines of the coefficient, the \({{L}_{p}}\)-interaction of a finite and an infinite singular points of a weak solution to the Dirichlet problem is studied in a class of functions with the first derivatives from \({{L}_{p}}(\Omega )\) in the entire range of the exponent \(p \in (1,\infty )\).
About the authors
A. M. Bogovskii
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Author for correspondence.
Email: abogovski@gmail.com
Russian Federation, Moscow, 119991
V. N. Denisov
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Author for correspondence.
Email: vdenisov2008@yandex.ru
Russian Federation, Moscow, 119991
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