Geodesic
Direct and inverse problems for the simple layer logarithmic potential
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 3-14

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With the help of Cauchy-type integrals, a new derivation of integral equations for solving logarithmic potential problems is given. The inverse problem is analyzed with two star-shaped solutions containing a smaller number of parameters than in the more difficult similar examples of I. M. Rapoport. The criterion of conversion to the identical constant of the internal potential of a simple layer is proved.
Keywords: logarithmic potential of a simple layer, convexity and star-like conditions, Cauchy-type integral. 
@article{IVM_2020_11_a0,
     author = {N. R. Abubakirov and L. A. Aksent'ev},
     title = {Direct and inverse problems for the simple layer logarithmic potential},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--14},
     publisher = {mathdoc},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_11_a0/}
}
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N. R. Abubakirov; L. A. Aksent'ev. Direct and inverse problems for the simple layer logarithmic potential. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2020_11_a0/