Geodesic
A certain property of solutions of parabolic equations with measurable coefficients
Izvestiya. Mathematics, Tome 16 (1981) no. 1, pp. 151-164 
N. V. Krylov; M. V. Safonov. A certain property of solutions of parabolic equations with measurable coefficients. Izvestiya. Mathematics, Tome 16 (1981) no. 1, pp. 151-164. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper Harnack's inequality is proved and the Hölder exponent is estimated for solutions of parabolic equations in nondivergence form with measurable coefficients. No assumptions are imposed on the smallness of scatter of the eigenvalues of the coefficient matrix for the second derivatives. Bibliography: 9 titles.

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

[3] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971 | MR

[4] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[5] Kordes G. O., “O pervoi kraevoi zadache dlya kvazilineinykh differentsialnykh uravnenii bolee chem s dvumya peremennymi”, Matematika, 3:2 (1959), 75–107

[6] Gusman M., Differentsirovanie integralov v $R^n$, Mir, M., 1978 | MR

[7] Krylov N. V., “Posledovatelnosti vypuklykh funktsii i otsenki maksimuma resheniya parabolicheskogo uravneniya”, Sib. matem. zhurnal, 17:2 (1976), 290–303 | MR | Zbl

[8] Krylov N. V., “O printsipe maksimuma dlya lineinykh parabolicheskikh i ellipticheskikh uravnenii”, Izv. AN SSSR. Ser. matem., 42 (1978), 1050–1062 | MR | Zbl