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