Growth property for the minimal surface equation in unbounded domains

Hwang, Jenn-Fang

doi:10.1090/S0002-9939-1994-1204379-X

Growth property for the minimal surface equation in unbounded domains
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by Jenn-Fang Hwang PDF

Proc. Amer. Math. Soc. 121 (1994), 1027-1037 Request permission

Abstract:

Here we prove that if u satisfies the minimal surface equation in an unbounded domain $\Omega$ which is properly contained in a half plane, then the growth rate of u is of the same order as the shape of $\Omega$ and $u{|_{\partial \Omega }}$.

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Vorlesungen über Minimalflächen

Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR 0256278
Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861