Analysis of Boundary Integral Equations for Laplace Dirichlet Bvp In 2d
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Date
2016-08-04
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Addis Ababa University
Abstract
Using an appropriate fundamental solution, Dirichlet boundary value problem is reduced
to some direct Boundary Integral Equations (BIEs). Although the theory of BIEs in 3D
is well developed, the BIEs in 2D need a special consideration due to their di_erent
equivalence properties. Consequently, we need to set conditions on the domain for
the invertibility of corresponding fundamental based integral layer potentials and hence
the unique solvability of BIEs. The properties of corresponding potential operators are
investigated. The equivalence of the original BVP and the obtained BIEs are analyzed
and the invertibility of the BIE operators is proved.
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Keywords
Analysis of Boundary, Integral Equations, Laplace Dirichlet Bvp In 2d