Geodesic
On local estimates near the boundary of solutions of a second order equation with nonnegative characteristic form
Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 715-735 
L. I. Kamynin; B. N. Khimchenko. On local estimates near the boundary of solutions of a second order equation with nonnegative characteristic form. Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 715-735. http://geodesic.mathdoc.fr/item/SM_1978_34_6_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Using barrier functions the authors study the connection between the geometric configuration of a domain, the order of degeneracy of the highest coefficients of an equation (near the boundary) and the behavior of solutions of these equations near the boundary of the domain of continuity of the solutions. The results obtained can be applied first to study local regularity of solutions near the boundary and secondly to theorems of Giraud type on the sign of the oblique derivative at boundary points when the solution attains its extremal values. Bibliography: 10 titles.

[1] C. Pucci, “Sulle funzioni barriera”, Matematiche, 18:1 (1957), 25–43 | MR

[2] C. Pucci, “Regolarita alia frontiere di soluzioni di equazioni ellitiche”, Ann. mat. pura appl., 65:4 (1964), 311–328 | MR | Zbl

[3] Y. R. Cannon, “Regularity at the boundary for solution of linear parabolic differential equations”, Ann. Scuola norm, super. Pisa, Sci. fis. e mat., 19:3 (1965), 415–427 | MR | Zbl

[4] L. I. Kamynin, “Printsip maksimuma i granichnye $\alpha$-otsenki reshenii pervoi kraevoi zadachi dlya parabolicheskogo uravneniya v netsilindricheskoi oblasti”, ZhVM i MF, 7:3 (1967), 551–567 | MR | Zbl

[5] L. I. Kamynin, B. N. Khimchenko, “Teoremy tipa Zhiro dlya uravneniya $2$-go poryadka so slabo vyrozhdayuscheisya neotritsatelnoi kharakteristicheskoi chastyu”, Sib. matem. zh., XVIII:1 (1977), 103–121 | MR

[6] L. I. Kamynin, B. N. Khimchenko, “O granichnykh otsenkakh Lipshitsa dlya reshenii elliptiko-parabolicheskogo uravneniya $2$-go poryadka”, DAN SSSR, 212:3 (1973), 544–547 | MR | Zbl

[7] L. I. Kamynin, B. N. Khimchenko, “Printsip maksimuma i granichnye otsenki Lipshitsa dlya reshenii elliptiko-parabolicheskogo uravneniya $2$-go poryadka”, Sib. matem. zh., XV:2 (1974), 343–367 | MR

[8] L. I. Kamynin, B. N. Khimchenko, “Printsip maksimuma i lokalnaya regulyarnost (v smysle Lipshitsa) reshenii parabolicheskogo uravneniya $2$-go poryadka vblizi bokovoi chasti parabolicheskoi granitsy”, DAN SSSR, 219:4 (1974), 785–788 | MR | Zbl

[9] L. I. Kamynin, B. N. Khimchenko, “Printsip maksimuma i lokalnye otsenki Lipshitsa vblizi bokovoi granitsy dlya reshenii parabolicheskogo uravneniya $2$-go poryadka”, Sib. matem. zh., XVI:6 (1975), 1172–1187 | MR

[10] R. Kurant i D. Gilbert, Metody matematicheskoi fiziki, t. 1, Gostekhizdat, Moskva–Leningrad, 1951