Analysis Of Boundary-domain Integral Equations For Variable Coefficient (the Case Of Dirichelet Bvp In 2d)

Using an appropriate parametrix (Levi function), Dirichlet boundary value problem is reducedrnto some direct segregated systems of Boundary- Domain Integral Equations (BDIEs).rnAlthough the theory of BDIEs in 3D is well developed, the BDIEs in 2D need a specialrnconsideration due to their different equivalence properties. Consequently, we needrnto set conditions on the domain or the spaces to insure the invertibility of correspondingrnparametrix-based integral layer potentials and hence the unique solubility of BDIEs.rnThe properties of corresponding potential operators are investigated. The equivalence ofrnthe original BVP and the obtained BDIEs are analysed and the invertibility of the BDIErnoperators is proved.

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