Catenoid-like solutions for the minimal surface equation

Jenn-Fang Hwang

Vol. 183 (1998), No. 1, 91–102

DOI: 10.2140/pjm.1998.183.91

Abstract

Let Ω ⊂ ℝ² be an unbounded domain with width of polynomial growth and let u satisfy the minimal surface equation in Ω. We find out an upper bound function for u and give an example to illustrate that the upper bound function obtained here is approximately optimal. In fact, the graph of the upper bound function is a generalization of a catenoid.

Milestones

Received: 15 January 1996

Revised: 9 October 1996

Published: 1 March 1998