Calculus of Variations and Geometric Measure Theory

L. Kreutz - B. Schmidt

A note on the Winterbottom Shape

created by kreutz on 21 Jan 2025

[BibTeX]

Published Paper

Inserted: 21 jan 2025
Last Updated: 21 jan 2025

Journal: Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Pages: 14
Year: 2025

Abstract:

In this short note we review results on equilibrium shapes of minimizers to the sessile drop problem. More precisely, we study the Winterbottom problem and prove that the Winterbottom shape is indeed optimal. The arguments presented here are based on relaxation and the (anisotropic) isoperimetric inequality.

Keywords: wetting, Interfacial energies, crystallization, dewetting, Winterbottom shape, capillarity problems


Download: