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A Phragmén–Lindelöf principle for the equation of a surface of constant mean curvature

Published online by Cambridge University Press:  14 November 2011

R. J. Knops  and
L. E. Payne
R. J. Knops
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K.
L. E. Payne
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853, U.S.A.
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Abstract

This paper studies the surface of constant mean curvature on a semi-infinite strip, and shows by means of a first-order differential inequality that the solution in a given measure either becomes asymptotically unbounded at least to polynomial order, or decays at most exponentially to the solution of an associated one-dimensional problem. A proof is also presented for uniqueness in the class of functions having bounded gradient and subject to specified growth conditions for large values of the longitudinal distance. Extensions of these results to the whole strip and to more general types of equations are also described.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 105 - 119
Copyright
Copyright © Royal Society of Edinburgh 1994

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