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 remark on strong maximum principle for parabolic and elliptic systems

Author: Xuefeng Wang
Journal: Proc. Amer. Math. Soc. 109 (1990), 343-348
MSC: Primary 35B50; Secondary 35J60, 35K55
MathSciNet review: 1019284
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a strong maximum principle for some nonlinear parabolic and elliptic systems with convex invariant regions. We also obtain a version of the Hopf boundary lemma for the systems.

References [Enhancements On Off] (What's this?)

  • [1] H. Weinberger, Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Mat. (7) 8 (1975), 295-310. MR 0397126 (53:986)
  • [2] K. Chueh, C. Conley and J. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J. 26 (1977), 373-392. MR 0430536 (55:3541)
  • [3] D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Heidelberg, 1983. MR 737190 (86c:35035)
  • [4] W. Troy, Summary properties in systems of semilinear elliptic equations, J. Differential Equations 42 (1981), 400-413. MR 639230 (83b:35051)
  • [5] J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304-318. MR 0333220 (48:11545)
  • [6] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243. MR 544879 (80h:35043)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35B50, 35J60, 35K55

Retrieve articles in all journals with MSC: 35B50, 35J60, 35K55

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society