Geodesic
On the maximum principle for nonlinear parabolic and elliptic equations
Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 335-347

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A maximum principle in Sobolev spaces is proved for nonlinear elliptic and parabolic equations. The proof is based on estimates for the maximum of the solutions of a parabolic equation with measurable coefficients, in terms of the $\mathscr L_p$ norm of the right side. The results of the paper are analogous to results of A. D. Aleksandrov on elliptic equations. Bibliography: 10 titles. 
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     author = {N. V. Krylov},
     title = {On the maximum principle for nonlinear parabolic and elliptic equations},
     journal = {Izvestiya. Mathematics },
     pages = {335--347},
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     volume = {13},
     number = {2},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a6/}
}
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N. V. Krylov. On the maximum principle for nonlinear parabolic and elliptic equations. Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 335-347. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a6/