Catenoid-like solutions for the minimal surface equation (Q1392498)

The author improves his Phragmèn-Lindelöf type theorems for solutions of the minimal surface equation, for domains suitably contained in a half plane [Proc. Am. Math. Soc. 121, 1027-1037 (1994; Zbl 0820.35010)]. Let \(\Omega\) be an unbounded domain with width of polynomial growth and let \(u\) satisfy the minimal surface equation in \(\Omega\). The author finds out an upper bound function for \(u\) and gives 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.