Geodesic
On the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations
Sbornik. Mathematics, Tome 11 (1970) no. 4, pp. 507-528 
V. I. Feigin. On the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations. Sbornik. Mathematics, Tome 11 (1970) no. 4, pp. 507-528. http://geodesic.mathdoc.fr/item/SM_1970_11_4_a2/
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     title = {On~the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations},
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     volume = {11},
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     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_4_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the question of smoothness for solutions of the first and second boundary problems for a class of degenerate equations (including, in particular, a parabolic equation) in domains with boundaries containing characteristic points. In the case of tangency of higher degree of the boundary with a characteristic plane conditions are given which guarantee that the solution belongs to the space $H_p$. Bibliography: 9 titles.

[1] J. J. Kohn, L. Nirenberg, “Degenerate elliptic-parabolic equations of second order”, Comm. Pure Appl. Math., 20:4 (1967), 797–872 | DOI | MR | Zbl

[2] O. A. Oleinik, “O lineinykh uravneniyakh vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Matem. sb., 69(111) (1966), 111–140 | MR | Zbl

[3] V. A. Kondratev, “Kraevye zadachi dlya parabolicheskikh uravnenii v zamknutykh oblastyakh”, Trudy Mosk. matem. ob-va, 15 (1967), 400–451

[4] Dzh. Dzh. Kon, L. Nirenberg, Nekoertsitivnye kraevye zadachi, Psevdodifferentsialnye operatory, Mir, Moskva, 1967 | MR

[5] V. P. Mikhailov, “O zadache Dirikhle dlya parabolicheskogo uravneniya”, Matem. sb., 61(103) (1963), 40–64

[6] E. V. Radkevich, “Vtoraya kraevaya zadacha dlya uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Vestnik MGU, matem. mekh., 1967, no. 4, 3–11

[7] L. Khermander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, Moskva, 1967

[8] L. Nirenberg, F. Trevs, “Solvability of a first order linear partial differential equation”, Comm. Pure Appl. Math., 16:3 (1963), 331–351 | DOI | MR | Zbl

[9] F. Dzhon, L. Beps, M. Shextep, Uravneniya s chastnymi proizvodnymi, Mir, Moskva, 1966 | MR