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|Title:||Analysis of some localized boundary-domain integral equations|
|Keywords:||Partial Differential Equations;Variable coefficients;Boundary value problems;Parametrix;Localized Boundary-Domain Integral Equations;Pseudo-differential operators|
|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|
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