Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the minimality of the Winterbottom shape

Shokhrukh Yu. Kholmatov

Abstract

In this short note we prove that the Winterbottom shape [Winterbottom: Acta Metallurgica (1967)] is a volume-constraint minimizer of the corresponding anisotropic capillary functional.

On the minimality of the Winterbottom shape

Abstract

In this short note we prove that the Winterbottom shape [Winterbottom: Acta Metallurgica (1967)] is a volume-constraint minimizer of the corresponding anisotropic capillary functional.
Paper Structure (2 sections, 1 theorem, 34 equations)

This paper contains 2 sections, 1 theorem, 34 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['teo:main']}

Key Result

Theorem 1.1

For any $\beta\in(-\Phi(-\mathbf{e}_n),\Phi(\mathbf{e}_n))$ The equality holds if and only if $E = W^\Phi(b - \beta \mathbf{e}_n)$ for some $b\in\partial\Omega.$ Equivalently, and the equality holds if and only if $E = \Omega\cap(b - r\beta\mathbf{e}_n + rW^\Phi)$ for some $r>0$ and $b\in \partial\Omega.$

Theorems & Definitions (1)

  • Theorem 1.1