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Title: Analysis of some localized boundary-domain integral equations
Authors: Chkadua, O
Mikhailov, SE
Natroshvili, D
Keywords: Partial Differential Equations;Variable coefficients;Boundary value problems;Parametrix;Localized Boundary-Domain Integral Equations;Pseudo-differential operators
Issue Date: 2009
Publisher: Rocky Mountain Mathematics Consortium
Citation: Journal of Integral Equations and Applications. 21 (3) 405-445
Abstract: Some direct segregated localized boundary-domain integral equation (LBDIE) systems associated with the Dirichlet and Neumann boundary value problems (BVP) for a scalar "Laplace" PDE with variable coefficient are formulated and analysed. The parametrix is localized by multiplication with a radial localizing function. Mapping and jump properties of surface and volume integral potentials based on a localized parametrix and constituting the LBDIE systems are studied in a scale of Sobolev (Bessel potential) spaces. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the LBDIE operators in the corresponding Sobolev spaces.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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