Geodesic
Boundary Problems for a Elliptical Second Order Equations
Trudy Instituta matematiki, Tome 15 (2007) no. 2, pp. 38-47.

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We consider boundary problems for linear elliptic second order equations using the method of energy inequalities and mollifiers with variable step. In particular, here are considered problems with boundary conditions along tangents of directions. The boundary of domain on which conditions are set, can be piecewise smooth. The theorems of existence of generalized solutions of considered problems are proved. 
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V. I. Korzyuk; E. S. Cheb. Boundary Problems for a Elliptical Second Order Equations. Trudy Instituta matematiki, Tome 15 (2007) no. 2, pp. 38-47. http://geodesic.mathdoc.fr/item/TIMB_2007_15_2_a4/

[1] Rempel Sh., Shultse B.-V., Teoriya indeksa ellipticheskikh zadach, Mir, M., 1986 | MR | Zbl

[2] Kondratev V.A., Oleinik O.A., “Kraevye zadachi dlya uravnenii s chastnymi proizvodnymi v negladkikh oblastyakh”, Uspekhi matem. nauk, 38:2 (1983), 3–76 | MR

[3] Nazarov S.A., Plamenevskii B.A., Ellipticheskie zadachi v oblastyakh s kusochno gladkoi granitsei, Nauka, M., 1991

[4] Grisvard P., Elliptic Problems in Non Smooth Domains, Pirman, Boston, 1985

[5] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[6] Schecher M., “Remarks on elliptic boundary value problems”, Comm. Pure Appl. Math., 12 (1959), 561–578 | DOI | MR

[7] Schecher M., “Mixed boundary problems for general elliptic equations”, Comm. Pure Appl. Math., 13 (1960), 183–201 | DOI | MR

[8] Sergienko I.V., Deineka V.S., “Optimalnoe upravlenie ellipticheskoi sistemy s nesimmetrichnym operatorom sostoyaniya”, Kibernetika i sistemnyi analiz, 6, 2005, 67–115 | MR

[9] Agmons, Duglis A., Nirenberg L., Otsenki vblizi granitsy dlya reshenii ellipticheskikh uravnenii v chastnykh proizvodnykh, udovletvoryayuschikh obschim granichnym usloviyam, Mir, M., 1965

[10] Korzyuk V.I., “Operatory osredneniya s peremennym shagom v teorii razreshimosti ellipticheskikh zadach”, Dokl. NAN Belarusi, 49:6 (2005), 25–38 | MR

[11] Mikhailov V.P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR | Zbl

[12] Ladyzhenskaya O.F., Uraltseva N.N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[13] Burenkov V.I., Sobole Spaces on Domains, Sttutgart-Leipzig, 1998 | MR

[14] Korzyuk V.I., “Ob operatorakh osredneniya s peremennym shagom. I.”, Vestn. Belorus. gos. un-ta. Ser. 1, 1992, no. 2, 49–53 | MR | Zbl

[15] Korzyuk V.I., “Ob operatorakh osredneniya s peremennym shagom. II”, Vestn. Belorus. gos. un-ta. Ser. 1, 1992, no. 3, 63–65 | MR | Zbl