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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some maximum principles in semilinear elliptic equations
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by Philip W. Schaefer PDF
Proc. Amer. Math. Soc. 98 (1986), 97-102 Request permission

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.
References
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  • Wen Duan Lu and Zhi Huo Yiang, Some results on maximum principles, Sichuan Daxue Xuebao 1 (1981), 23–36 (Chinese, with English summary). MR 670546
  • L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math. Special Issue Special Issue (1968/69), part I, 51–59. Special issue presented to Professor Bibhutibhusan Sen on the occasion of his seventieth birthday, Part I. MR 0351225
  • M. H. Protter and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana Univ. Math. J. 23 (1973/74), 239–249. MR 324204, DOI 10.1512/iumj.1973.23.23020
    • M. H. Protter, Gradient bounds for a class of second order elliptic equations, Contemp. Math. 11 (1982), 191-198.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 98 (1986), 97-102
  • MSC: Primary 35B50; Secondary 35J60
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0848884-X
  • MathSciNet review: 848884