The planar Plateau's problem via capillarity

TL;DR

This paper explores a capillarity-based model for the classical Plateau's problem, incorporating nonlocal effects to better understand soap film behavior and address physical phenomena like collapsing.

Contribution

It introduces a nonlocal geometric potential into the variational framework, offering a novel approach to modeling soap films with thickness effects.

Findings

Incorporates thickness effects into soap film modeling

Addresses collapsing phenomena in soap films

Provides new insights into physical properties of soap films

Abstract

The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the problem and study a soap film model in the spirit of capillarity formulations in two dimensions. Our approach introduces a nonlocal geometric potential in the variational length minimization scheme. This incorporates effects of thickness of soap films and provides insight into addressing the so-called collapsing phenomenon and other observable physical phenomena and properties.