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

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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. 
@article{SM_1970_11_4_a2,
     author = {V. I. Feigin},
     title = {On~the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations},
     journal = {Sbornik. Mathematics},
     pages = {507--528},
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     volume = {11},
     number = {4},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_4_a2/}
}
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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/