Existence and Regularity of Minimizers for a Plateau Approximation Problem

Abstract: In this paper, we study the functional introduced by the author in collaboration with Bonnivard, Bretin, and Lemenant, which is designed to approximate Plateau's problem. We establish the existence of a minimizer and prove its H{ö}lder regularity. Our results may be viewed as a generalization to higher-dimensional surfaces of the one-dimensional work of Bonnivard, Lemenant, and Millot on the approximation of the Steiner problem.