Existence and C0, α regularity of minima of a functional related to the grid-generation problem

The existence of C0,α regularity of minima of a functional arising from the grid-generation problem are provided in the case of n-dimensional domains. The functional studied in this article is a linear combination of the length functional, the volume functional, and a higher-order term. The inclusion of the latter guarantees the existence and regularity of a minimum via the direct method for calculus of variations. © 1993 John Wiley & Sons, Inc.