Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/3358
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/3358 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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