Phragmèn–Lindelöf theorem for minimal surface equations in higher dimensions

Chun-Chung Hsieh, Jenn-Fang Hwang and Fei-Tsen Liang

Vol. 207 (2002), No. 1, 183–198

DOI: 10.2140/pjm.2002.207.183

Abstract

Here we prove that if u satisfies the minimal surface equation in an unbounded domain which is properly contained in a half space of ℝⁿ, with n ≥ 2, then the growth rate of u is of the same order as that of the shape of Ω and the boundary value of u.

Milestones

Received: 27 February 2001

Published: 1 November 2002