Geodesic
On modified Bitsadze--Samarskiy problem
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2007), pp. 10-15.

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We study the non-local boundary value problem which is an analogue of the Bitsadze–Samarskiy problem. For the two-dimensional case we reduce this problem to the local boundary value problem, more exactly to the Dirichlet problem for the analogue of the Laplace equation on the stratified set. Using the Poincare–Perron method we establish that the solution is the upper envelope of the set of subharmonic functions taking given values on the boundary. 
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L. A. Kovaleva. On modified Bitsadze--Samarskiy problem. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2007), pp. 10-15. http://geodesic.mathdoc.fr/item/VSGTU_2007_1_a1/

[1] Bitsadze A. V., Samarskii A. A., “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh kraevykh zadach”, Dokl. AN SSSR, 185 (1969), 739–740 | Zbl

[2] Fam F., Vvedenie v topologicheskoe issledovanie osobennostei Landau, Mir, M., 1970

[3] Penkin O., “About a geometrical approach to multistructures and some qualitative properties of solutions”, Partial Differential Equations on Multistructures, Lect. Notes Pure Appl. Math., 219, eds. F. Ali Mehmeti, J. von Below, S. Nicaise, 2001, 183–192 | MR

[4] Penkin O. M., “Second-order elliptic equations on a stratified set. Differential equations on networks”, J. Math. Sci., 119:6 (2004), 836–867 | DOI | MR | Zbl

[5] Penkin O. M., Bogatov E. M., “O slaboi razreshimosti zadachi Dirikhle na stratifitsirovannykh mnozhestvakh”, Matem. zametki, 68:6 (2000), 874–886 | DOI | MR | Zbl

[6] Penkin O. M., Pokornyi Yu. V., “O differentsialnykh neravenstvakh dlya ellipticheskikh uravnenii na slozhnykh mnogoobraziyakh”, Dokl. RAN, 360:4 (1998), 456–458 | MR | Zbl

[7] Nicaise S., Penkin O., “Poincare–Perron's method for the Dirichlet problem on stratified sets”, J. Math. Anal. Appl., 296:2 (2004), 504–520 | DOI | MR | Zbl

[8] John F., Partial Differential Equation, Springer-Verlag, 1986

[9] Gilbarg D., Trudinger M. N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[10] Kheiman U., Kennedi P., Subgarmonicheskie funktsii, Mir, M., 1980