On the maximum principle for nonlinear parabolic and elliptic equations

N. V. Krylov

doi:10.1070/IM1979v013n02ABEH002046

On the maximum principle for nonlinear parabolic and elliptic equations

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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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 language	English (US)
Pages (from-to)	335-347
Number of pages	13
Journal	Mathematics of the USSR - Izvestija
Volume	13
Issue number	2
DOIs	https://doi.org/10.1070/IM1979v013n02ABEH002046
State	Published - Apr 30 1979

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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.",

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On the maximum principle for nonlinear parabolic and elliptic equations

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