Geodesic
Finding of accessory parameters for mixed inverse boundary value problem with polygonal known part of boundary
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 34-40

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We consider a mixed inverse boundary value problem with respect to parameter $x$ for the case when the known part of the boundary $L_z^1$ is a polygonal line. Integral representation of solution to the problem depends on real parameters being the pre-images of the vertices of $L_z^1$ under conformal mapping. By analogy with Schwartz–Christoffel integrals, we name them accessory parameters. It is suggested a new method of determining the accessory parameters. Is is based on consideration of one-parametric family of solutions to the problem corresponding to the case when the known part of the boundary is the union of two rays and the stretching slit the endpoint of which goes along the given polygonal line $L_z^1$. 
@article{ISU_2011_11_4_a4,
     author = {S. R. Nasyrov and L. Yu. Nizamieva},
     title = {Finding of accessory parameters for mixed inverse boundary value problem with polygonal known part of boundary},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {34--40},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a4/}
}
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S. R. Nasyrov; L. Yu. Nizamieva. Finding of accessory parameters for mixed inverse boundary value problem with polygonal known part of boundary. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 34-40. http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a4/