On the Interaction of Boundary Singular Points in the Dirichlet Problem for an Elliptic Equation with Piecewise Constant Coefficients in a Plane Domain


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

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

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2019 Pleiades Publishing, Ltd.