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http://bura.brunel.ac.uk/handle/2438/7603
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 |
URI: | http://link.springer.com/article/10.1007%2Fs00020-013-2054-4 http://bura.brunel.ac.uk/handle/2438/7603 |
DOI: | http://dx.doi.org/10.1007/s00020-013-2054-4 |
ISSN: | 0378-620X |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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