Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0291634-9
MathSciNet review: 0291634
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] L. Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167-177. MR 14, 1089; MR 16, 1336. MR 0055544 (14:1089e)
  • [3] J. Serrin, On the strong maximum principle for quasilinear second order differential inequalities, J. Functional Analysis 5 (1970), 184-193. MR 41 #3966. MR 0259328 (41:3966)
  • [4] N. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205-226. MR 37 #1758. MR 0226168 (37:1758)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35K10

Retrieve articles in all journals with MSC: 35K10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291634-9
Keywords: Parabolic equations, quasilinear equations, strong maximum principle
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society