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Title: Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients
Authors: Chkadua, O
Mikhailov, SE
Natroshvili, D
Keywords: Partial differential equations;Variable coefficients;Boundary value problems;Localized parametrix;Localized potentials;Localized boundary-domain integral equations;Pseudo-differential equations
Issue Date: 2013
Publisher: Springer Basel
Citation: Integral Equations and Operator Theory, 76(4): 509-547, Aug 2013
Abstract: Employing the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and Robin boundary value problems 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 boundary value problems 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.
Description: This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer Basel
ISSN: 0378-620X
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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