Geodesic
Local uniqueness of solution of a mixed boundary value problem for Riemann surfaces with branch-points
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 97-108

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A mixed boundary value problem for Riemann surfaces with branch-points, with boundary conditions depending on the parameter $x$ is investigated. Is is supposed that the known part of the boundary of the required surface is a polygon. We obtain an integral representation of solution to the problem; it depends on accessory parameters. Local uniqueness of the solution is proved. 
@article{UZKU_2006_148_2_a9,
     author = {S. R. Nasyrov and I. Z. Faizov},
     title = {Local uniqueness of solution of a~mixed boundary value problem for {Riemann} surfaces with branch-points},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {97--108},
     publisher = {mathdoc},
     volume = {148},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a9/}
}
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S. R. Nasyrov; I. Z. Faizov. Local uniqueness of solution of a mixed boundary value problem for Riemann surfaces with branch-points. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 97-108. http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a9/