A strong maximum principle for quasilinear parabolic differential inequalities
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Abstract:
A maximum principle for ${C^1}$ solutions of quasilinear parabolic differential inequalities which retains the strong conclusion of Nirenberg’s well-known result [2] is established. The case of strongly differentiable solutions rather than of class ${C^1}$ is also discussed.References
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E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, S.-B. Preuss. Akad. Wiss. 19 (1927), 147-152.
- Louis Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167–177. MR 55544, DOI 10.1002/cpa.3160060202
- James Serrin, On the strong maximum principle for quasilinear second order differential inequalities, J. Functional Analysis 5 (1970), 184–193. MR 0259328, DOI 10.1016/0022-1236(70)90024-8
- Neil S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205–226. MR 226168, DOI 10.1002/cpa.3160210302
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 497-502
- MSC: Primary 35K10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291634-9
- MathSciNet review: 0291634