Localized boundary-domain singular integral equations of the Robin type problem for self-adjoint second-order strongly elliptic PDE systems-Reference-Cited by-同舟云学术

Localized boundary-domain singular integral equations of the Robin type problem for self-adjoint second-order strongly elliptic PDE systems

Published:2020-11-12 Issue:5 Volume:28 Page:695-715
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Chkadua Otar¹,Mikhailov Sergey²,Natroshvili David³

Affiliation:

1. A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University , 6, Tamarashvili Str., 0177; and Sokhumi State University, 9 Politkovskaia Str. , Tbilisi 0186 , Georgia

2. Department of Mathematics , Brunel University London , Uxbridge UB8 3PH , United Kingdom

3. Department of Mathematics , Georgian Technical University , 77, Kostava Str., 0175; and I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2 University Str. , Tbilisi 0186 , Georgia

Abstract

Abstract The paper deals with the three-dimensional Robin type boundary-value problem (BVP) for a second-order strongly elliptic system of partial differential equations in the divergence form with variable coefficients. The problem is studied by the localized parametrix based potential method. By using Green’s representation formula and properties of the localized layer and volume potentials, the BVP under consideration is reduced to the a system of localized boundary-domain singular integral equations (LBDSIE). The equivalence between the original boundary value problem and the corresponding LBDSIE system is established. The matrix operator generated by the LBDSIE system belongs to the Boutet de Monvel algebra. With the help of the Vishik–Eskin theory based on the Wiener–Hopf factorization method, the Fredholm properties of the corresponding localized boundary-domain singular integral operator are investigated and its invertibility in appropriate function spaces is proved.

Funder

Shota Rustaveli National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2020-2082/pdf

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