ANALYSIS OF SOME LOCALIZEDBOUNDARY-DOMAIN INTEGRAL EQUATIONS

摘要

Some direct segregated localized boundary-domain integral equation (LBDIE) systems associated withthe Dirichlet and Neumann boundary value problems (BVP)for a scalar "Laplace" PDE with variable coefficient are for-mulated and analysed. The parametrix is localized by multi-plication with a radial localizing function. Mapping and jumpproperties of surface and volume integral potentials based on alocalized parametrix and constituting the LBDIE systems arestudied in a scale of Sobolev (Bessel potential) spaces. Themain results established in the paper are the LBDIEs equiva-lence to the original variable-coefficient BVPs and the invert-ibility of the LBDIE operators in the corresponding Sobolevspaces.