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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A strong maximum principle for quasilinear parabolic differential inequalities


Author: O. ARENA
Journal: Proc. Amer. Math. Soc. 32 (1972), 497-502
MSC: Primary 35K10
MathSciNet review: 0291634
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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 [Enhancements On Off] (What's this?)

  • [1] E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, S.-B. Preuss. Akad. Wiss. 19 (1927), 147-152.
  • [2] Louis Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167–177. MR 0055544 (14,1089e)
  • [3] James Serrin, On the strong maximum principle for quasilinear second order differential inequalities, J. Functional Analysis 5 (1970), 184–193. MR 0259328 (41 #3966)
  • [4] Neil S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205–226. MR 0226168 (37 #1758)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0291634-9
PII: S 0002-9939(1972)0291634-9
Keywords: Parabolic equations, quasilinear equations, strong maximum principle
Article copyright: © Copyright 1972 American Mathematical Society