International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 2, Pages 341-361
doi:10.1155/S0161171283000307

On solving the plateau problem in parametric form

Baruch cahlon,1 Alan D. Solomon,2 and Louis J. Nachman3

 1Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USA
2Mathematics and Statistics Research Division, Computer Science Division, Union Carbide Corporation-Nuclear Division, Oak Ridge 37830, Tennessee, USA
3Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USA
Received 15 August 1980; Revised 6 February 1981

Abstract

This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.