This article is cited in 12 papers

On the maximum principle for nonlinear parabolic and elliptic equations

N. V. Krylov


Abstract: 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.

UDC: 517.9

MSC: Primary 35K55; Secondary 35B45, 35J60

Received: 11.05.1977

 English version: Mathematics of the USSR-Izvestiya, 1979, 13:2, 335–347

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