First boundary-value problem for second-order elliptic-parabolic equations with discontinuous coefficients
Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 39 (2011), pp. 102-129.

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In this paper, the first boundary value problem for the second-order degenerated ellipticparabolic equations in nondivergent form is considered. Unique strong (almost everywhere) solvability of this problem in the corresponding weight Sobolev space is proved.
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I. T. Mamedov. First boundary-value problem for second-order elliptic-parabolic equations with discontinuous coefficients. Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 39 (2011), pp. 102-129. http://geodesic.mathdoc.fr/item/CMFD_2011_39_a5/

[1] Alkhutov Yu. A., Mamedov I. T., “Nekotorye svoistva reshenii pervoi kraevoi zadachi dlya parabolicheskikh uravnenii s razryvnymi koeffitsientami”, DAN SSSR, 284:1 (1985), 11–16 | MR | Zbl

[2] Alkhutov Yu. A., Mamedov I. T., “Pervaya kraevaya zadacha dlya nedivergentnykh parabolicheskikh uravnenii vtorogo poryadka s razryvnymi koeffitsientami”, Mat. cb., 131(173):4 (1986), 477–500 | MR | Zbl

[3] Keldysh M. V., “O nekotorykh sluchayakh vyrozhdeniya uravnenii ellipticheskogo tipa na granitse oblasti”, DAN SSSR, 77:2 (1951), 181–183

[4] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

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

[6] Mamedov I. T., Guseinov G. T., “O razreshimosti pervoi kraevoi zadachi dlya vyrozhdennykh elliptichesko-parabolicheski uravnenii vtorogo poryadka”, Dokl. AN Azerb., 1:3 (2000), 30–39 | MR

[7] Oleinik O. A., Radkevich E. V., Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi, VINITI, M., 1971

[8] Canfora A., “Esistenza ed unicita delle soluzioni di un problema al contorno relativo ad un' equazione elliptico-parabolica di ordine $2m$”, Recerche Mat., 25 (1976), 247–304 | MR | Zbl

[9] Cordes H. O., “Über die erste randwertaufgabe bei quasilinearen differentialgleichungen zweiter ornung in mehr als zwei variablen”, Math. Ann., 131 (1956), 278–312 | DOI | MR | Zbl

[10] Courant R., Hilbert D., Methods of mathematical physics, v. II, Interscience, New York, 1962 | Zbl

[11] Fichera G., “On a unified theory of boundary value problems of elliptic-parabolic equations of second order”, Boundary Probl. in Differ. Equations, Proc. Sympos. (Madison, April 20–22, 1959), 1960, 97–120 | MR | Zbl

[12] Fiorito G., “Un contributo alla risoluzione del problema di Cauchy–Dirichlet”, Matematiche, 35 (1980), 53–70 | MR

[13] Franciosi M., “Sul di un'equazione ellittico-parabolica a coefficienti discontinui”, Boll. Un. Mat. Ital. C (6), 2 (1983), 63–75 | MR | Zbl

[14] Franciosi M., “Un teorema di esistenza ed unicita per la soluzione di un'equazione ellittico-parabolica, a coefficienti discontinui, in forma non divergenza”, Boll. Un. Mat. Ital. B (6), 4 (1985), 253–263 | MR | Zbl

[15] Hardy G. H., Littlewood J. E., Polya G., Inequalities, Camdridge Univ. Press, Cambridge, 1952 | MR | Zbl

[16] Kohn J. J., Nirenberg L., “Degenerate elliptic-parabolic equations of second order”, Comm. Pure Appl. Math., 20 (1967), 797–872 | DOI | MR | Zbl

[17] Mamedov I. T., “An inequality of A. D. Aleksandrov type for degenerate elliptic-parabolic operators of second order”, Proc. Inst. Math. Mech. Nat. Acad. Sci. Azerb., 13, 2000, 92–96 | MR | Zbl

[18] Mamedov I. T., Agayeva R. A., “The first boundary value problem for nondivergent linear second order elliptic equations of Cordes type”, Trans. Nat. Acad. Sci. Azerb., 22:1 (2002), 150–167 | MR | Zbl

[19] Mamedov I. T., Muradov T. R., “On the Dirichlet problem for the Gilbarg–Serrin equation”, Proc. Inst. Math. Mech. Nat. Acad. Sci. Azerb., 16, 2002, 81–93 | MR | Zbl

[20] Mamedov I. T., Salmanova Sh. Yu., “The A. D. Aleksandrov type inequality for a class of second order equations with non-negative characteristic form”, Trans. Nat. Acad. Sci. Azerb., 21:4 (2001), 108–114 | MR

[21] Salmanova Sh. Yu., “On solvability of the first boundary value problem fro the second order degenerate elliptic-parabolic equations”, Proc. Inst. Math. Mech. Nat. Acad. Sci. Azerb., 15, 2001, 132–145 | MR | Zbl

[22] Talenti G., “Sopra una classe di equazioni ellittiche a coefficienti misurableili”, Ann. Mat. Pura Appl., 69 (1965), 285–304 | DOI | MR | Zbl

[23] Wen G. C., “Initial-mixed boundary value problems for parabolic equations of second order with measurable coefficients in a higher dimensional domain”, Proceedings of the Second ISAAK Congress, v. I, Kluwer Acadmic Publishers, Dordrecht–Boston–London, 2000 | MR

[24] Wen G. C., Maoying T., “Initial-oblique derivative problems for nonlinear parabolic equations with measurable coefficients”, Comm. Nonlinear Sci. Numer. Simul., 2 (1998), 109–113 | DOI | MR | Zbl