Crystalline evolutions with rapidly oscillating forcing terms

TL;DR

This paper studies how crystalline shapes evolve under rapidly oscillating periodic forces, deriving the limiting behavior as oscillation frequency increases, revealing complex phenomena like pinning and depinning.

Contribution

It characterizes the limit evolution law for crystalline curvature flows in stratified media with oscillatory forcing, highlighting new properties and phenomena.

Findings

Limit evolution law derived as oscillation period tends to zero

Identified phenomena such as pinning and depinning

Discussed properties like uniqueness and comparison principles

Abstract

We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is very simple, the limit evolution problem is quite rich, and we discuss some properties such as uniqueness, comparison principle and pinning/depinning phenomena.