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Iterative methods for the reconstruction of an inverse potential problem. (English) Zbl 0858.35134
This paper studies the problem to determine the support of the forcing term from the knowledge of the Cauchy data on the boundary of the region. The first and second domain derivatives are characterized as boundary value problems. Then Newton- and Landweber-type methods are compared from both, the theoretical and numerical, point of view. Due to the illposedness of the problem, regularization strategies have to be imposed.

MSC:
35R30 Inverse problems for PDEs
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
65R30 Numerical methods for ill-posed problems for integral equations
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