Geodesic
The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 471-495

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This paper is concerned with the questions of solvability and smoothness of weak solutions of the first boundary value problem for a parabolic equation of the form $$ \mathscr Lu=\sum^n_{i,k=1}a_{ik}(t,x)u_{x_ix_k}-u_t=f(t,x). $$ Bibliography: 18 titles. 
@article{SM_1988_59_2_a12,
     author = {Yu. A. Alkhutov and I. T. Mamedov},
     title = {The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_2_a12/}
}
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Yu. A. Alkhutov; I. T. Mamedov. The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 471-495. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a12/