Analysis Of Boundary Integral Equations For Laplace Dirichlet Bvp In 2d

Using an appropriate fundamental solution, Dirichlet boundary value problem is reducedrnto some direct Boundary Integral Equations (BIEs). Although the theory of BIEs in 3Drnis well developed, the BIEs in 2D need a special consideration due to their di_erentrnequivalence properties. Consequently, we need to set conditions on the domain forrnthe invertibility of corresponding fundamental based integral layer potentials and hencernthe unique solvability of BIEs. The properties of corresponding potential operators arerninvestigated. The equivalence of the original BVP and the obtained BIEs are analyzedrnand the invertibility of the BIE operators is proved.

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