article

Title: Viscosity solutions for a polymer crystal growth model

Authors: Pierre Cardaliaguet, Olivier Ley and Aurelien Monteillet

Issue: Volume 60 (2011), Issue 3, 895-936

Abstract:

$We prove existence of a solution for a polymer crystal growth model describing the movement of a front $(\Gamma(t))$ evolving with a nonlocal velocity. In this model the nonlocal velocity is linked to the solution of a heat equation with source $\delta_{\Gamma}$. The proof relies on new regularity results for the eikonal equation, in which the velocity is positive but merely measurable in time and with H\"older bounds in space. From this result, we deduce \emph{a priori} regularity for the front. On the other hand, under this regularity assumption, we prove bounds and regularity estimates for the solution of the heat equation.$