Geodesic
On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 9, pp. 1587-1597

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The problem of determining the permittivity of material samples of arbitrary shape placed in a rectangular waveguide with perfectly conducting walls is investigated. The problem is reduced to solving a nonlinear volume singular integral equation. A theorem on the existence and uniqueness of solutions to the nonlinear volume singular integral equation and of the inverse boundary value problem for determining the permittivity of the material is proved. 
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     author = {D. A. Mironov and Yu. G. Smirnov},
     title = {On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {50},
     number = {9},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_9_a3/}
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D. A. Mironov; Yu. G. Smirnov. On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 9, pp. 1587-1597. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_9_a3/