Geodesic
The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 115-135
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We consider the mixed problem for Laplace's equation outside cuts in a plane. The Dirichlet boundary condition is posed on one side of each cut, and the skew derivative condition is posed on the other side. This problem generalizes the mixed Dirichlet–Neumann problem. Using the method of potentials, this problem is reduced to a uniquely solvable Fredholm integral equation of the second kind. 
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P. A. Krutitskii; A. I. Sgibnev. The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 115-135. http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a7/

[1] Gabov S. A., “Uglovoi potentsial i ego nekotorye prilozheniya”, Mat. sb., 103 (145):4 (1977), 490–504 | MR | Zbl

[2] Gosteva A. S., Krutitskaya N. Ch., Krutitskii P. A., “Smeshannaya zadacha v zamagnichennoi poluprovodnikovoi plenke s razrezami vdol pryamoi”, Fundament. i prikl. mat., 6:4 (2000), 1061–1073 | MR | Zbl

[3] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972

[4] Krutitskii P. A., “Zadacha Dirikhle dlya uravneniya Gelmgoltsa vne razrezov na ploskosti”, ZhVM i MF, 34:8–9 (1994), 1237–1258 | MR | Zbl

[5] Krutitskii P. A., “Zadacha Neimana dlya uravneniya Gelmgoltsa vne razrezov na ploskosti”, ZhVM i MF, 34:11 (1994), 1652–1665 | MR | Zbl

[6] Krutitskii P. A., “Smeshannaya zadacha dlya uravneniya Laplasa vne razrezov na ploskosti”, Differents. uravn., 33:9 (1997), 1181–1190 | MR | Zbl

[7] Krutitskii P. A., Sgibnev A. I., “Metod integralnykh uravnenii v smeshannoi zadache Dirikhle–Neimana dlya uravneniya Laplasa vne razrezov na ploskosti”, Differents. uravn., 37:10 (2001), 1299–1310 | MR | Zbl

[8] Lifanov I. K., Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment, TOO “Yanus”, M., 1995 | MR | Zbl

[9] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR | Zbl

[10] Funktsionalnyi analiz, ed. G. Krein, Nauka, M., 1964