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|Title:||About analysis of some localized boundary-domain integral equations for a variable-coefficient BVPs|
|Keywords:||partial differential equations; variable coefficients; parametrix; localisation; boundary-domain integral equation; pseudo-differential operators|
|Citation:||In: Trevelyan, J (ed). Advances in boundary integral methods - proceedings of the sixth UK conference on boundary integral methods. Durham University, 2007|
|Abstract:||Some direct localized boundary-domain integral equations (LBDIEs) associated with the Dirichlet and Neumann boundary value problems for the "Laplace" linear differential equation with a variable coefficient are formulated. The LBDIEs are based on a parametrix localized by a cut-off function. Applying the theory of pseudo-differential operators, invertibility of the localized volume potentials is proved first. This allows then to prove solvability, solution uniqueness and equivalence of the LBDIEs to the original BVP, and investigate the LBDIE operator invertibility in appropriate Sobolev spaces.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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