Geodesic
Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s equation in a piecewise homogeneous medium
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1476-1489 
S. V. Gavrilov; A. M. Denisov. Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s equation in a piecewise homogeneous medium. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1476-1489. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a10/
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     author = {S. V. Gavrilov and A. M. Denisov},
     title = {Numerical methods for determining the inhomogeneity boundary in a~boundary value problem for {Laplace{\textquoteright}s} equation in a~piecewise homogeneous medium},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A boundary value problem for Laplace’s equation in a bounded two-dimensional domain filled with a piecewise homogeneous medium is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem of determining the inhomogeneity boundary and the solution of the equation given the solution and its normal derivative on the boundary of the domain is discussed. Numerical methods are proposed for solving the inverse problem, and the results of numerical experiments are presented.

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