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 Cahlon1
, Alan D. Solomon2
and Louis J. Nachman1
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
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.