Localized Boundary-Domain Singular Integral Equations Based on Harmonic Parametrix for Divergence-Form Elliptic PDEs with Variable Matrix Coefficients

被引：0
作者：
O. Chkadua
S. E. Mikhailov
D. Natroshvili
机构：
[1] I.Javakhishvili Tbilisi State University,A.Razmadze Mathematical Institute
[2] Sokhumi State University,Department of Mathematics
[3] Brunel University London,Department of Mathematics
[4] Georgian Technical University,I. Vekua Institute of Applied Mathematics
[5] Tbilisi State University,undefined
来源：
Integral Equations and Operator Theory | 2013年 / 76卷
关键词：
35J25; 31B10; 45K05; 45A05; Partial differential equations; variable coefficients; boundary value problems; localized parametrix; localized potentials; localized boundary-domain integral equations; pseudo-differential equations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Employing the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and Robin boundary value problems (BVPs) for general variable-coefficient divergence-form second-order elliptic partial differential equations are reduced to some systems of localized boundary-domain singular integral equations. Equivalence of the integral equations systems to the original BVPs is proved. It is established that the corresponding localized boundary-domain integral operators belong to the Boutet de Monvel algebra of pseudo-differential operators. Applying the Vishik–Eskin theory based on the factorization method, the Fredholm properties and invertibility of the operators are proved in appropriate Sobolev spaces.
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页码：509 / 547
页数：38
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