On the maximum principle for nonlinear parabolic and elliptic equations

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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 norm of the right side. The results of the paper are analogous to results of A. D. Aleksandrov on elliptic equations. Bibliography: 10 titles.

Original languageEnglish (US)
Pages (from-to)335-347
Number of pages13
JournalMathematics of the USSR - Izvestija
Volume13
Issue number2
DOIs
StatePublished - Apr 30 1979

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