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Some maximum principles in semilinear elliptic equations

Author: Philip W. Schaefer
Journal: Proc. Amer. Math. Soc. 98 (1986), 97-102
MSC: Primary 35B50; Secondary 35J60
MathSciNet review: 848884
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Abstract: We develop maximum principles for functions defined on the solutions to a class of semilinear, second order, uniformly elliptic partial differential equations. These principles are related to recent theorems of Protter and Protter and Weinberger and to a technique initiated by Payne for the determination of gradient bounds on the solution of the equation.

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  • [1] C. Bandle, R. P. Sperb, and I. Stakgold, Diffusion and reaction with monotone kinetics, Nonlinear Anal. 8 (1984), 321-333. MR 739663 (85k:35085)
  • [2] Wen Duan Lu and Zhi Huo Yiang, Some results on maximum principles, Sichuan Daxue Xuebao (1981), 23-36. (Chinese) MR 670546 (84a:35031)
  • [3] L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math. (1968), 51-59. MR 0351225 (50:3714)
  • [4] M. H. Protter and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana Univ. Math. J. 23 (1973), 239-249. MR 0324204 (48:2556)
  • [5] M. H. Protter, Gradient bounds for a class of second order elliptic equations, Contemp. Math. 11 (1982), 191-198.
  • [6] R. P. Sperb, Maximum principles and nonlinear elliptic problems, J. Anal. Math. 35 (1979), 236-263. MR 555305 (81f:35044)
  • [7] -, Maximum principles and their applications, Academic Press, New York, 1981. MR 615561 (84a:35033)

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Keywords: Semilinear elliptic equations, maximum principles
Article copyright: © Copyright 1986 American Mathematical Society

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