Localized Boundary-Domain Singular Integral Equations of Dirichlet Problem for Self-adjoint Second Order Strongly Elliptic PDE Systems
Abstract
The paper deals with the three-dimensional Dirichlet boundary value problem (BVP) for a second order strongly elliptic self-adjoint system of partial differential equations in the divergence form with variable coefficients and develops the integral potential method based on a localized parametrix. Using Green's representation formula and properties of the localized layer and volume potentials, we reduce the Dirichlet BVP to a system of localized boundary-domain integral equations (LBDIEs). The equivalence between the Dirichlet BVP and the corresponding LBDIE system is studied. We establish that the obtained localized boundary-domain integral operator belongs to the Boutet de Monvel algebra. With the help of the Wiener-Hopf factorization method we investigate corresponding Fredholm properties and prove invertibility of the localized operator in appropriate Sobolev (Bessel potential) spaces.
Keywords
Cite
@article{arxiv.1510.04974,
title = {Localized Boundary-Domain Singular Integral Equations of Dirichlet Problem for Self-adjoint Second Order Strongly Elliptic PDE Systems},
author = {O. Chkadua and S. E. Mikhailov and D. Natroshvili},
journal= {arXiv preprint arXiv:1510.04974},
year = {2018}
}
Comments
31 pages, Math. Meth. Appl. Sci., 2016, 21p