Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga - E. Valdinoci

Curvature flow in heterogeneous media

created by novaga on 17 Mar 2010
modified on 09 Nov 2018


Published Paper

Inserted: 17 mar 2010
Last Updated: 9 nov 2018

Journal: Interfaces Free Bound.
Volume: 13
Number: 4
Pages: 485-505.
Year: 2011

ArXiv: 1003.3366 PDF


In recent years, there has been a growing interest in geometric evolution in heterogeneous media. Here we consider curvature driven fows of planar curves, with an additional space-dependent forcing term. Motivated by a homogenization problem, we look for estimates which depend only on the uniform norm of the forcing term. By means of an asymptotic analysis, we discuss the properties of the limit solutions of the homogenization problem, which we can rigorously solve in some special cases: that is, when the initial curve is a graph, and the forcing term does not depend on the vertical direction. As a by-product, in such cases we are able to define a soluton of the geometric evolution when the forcing term is just a bounded, not necessarily continuous, function.