Geodesic
On the smoothness of solutions of degenerate elliptic equations
Izvestiya. Mathematics , Tome 2 (1968) no. 6, pp. 1337-1359

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It is shown that under broad assumptions the generalized solution of boundary problems for degenerate second-order equations satisfies a Hölder condition. An example is given which shows that increasing the smoothness of the data of the problem cannot alone achieve greater smoothness of the solution. Conditions are determined for existence of the derivatives of the generalized solution. The investigation is based on probability methods. 
@article{IM2_1968_2_6_a7,
     author = {M. I. Freidlin},
     title = {On the smoothness of solutions of degenerate elliptic equations},
     journal = {Izvestiya. Mathematics },
     pages = {1337--1359},
     publisher = {mathdoc},
     volume = {2},
     number = {6},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_6_a7/}
}
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M. I. Freidlin. On the smoothness of solutions of degenerate elliptic equations. Izvestiya. Mathematics , Tome 2 (1968) no. 6, pp. 1337-1359. http://geodesic.mathdoc.fr/item/IM2_1968_2_6_a7/