# Viscosity solutions for a polymer crystal growth model

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1 LM - Laboratoire de mathématiques de Brest 2 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : We prove existence of a solution for a polymer crystal growth model describing the movement of a front $\Gammat$ 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\-{o}lder bounds in space. From this result, we deduce \textit{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.

Keywords : heat equation Nonlocal Hamilton-Jacobi Equations nonlocal front propagation level-set approach geometrical properties lower-bound gradient estimate viscosity solutions eikonal equation heat equation.

Autor: Pierre Cardaliaguet - Olivier Ley - Aurélien Monteillet -

Fuente: https://hal.archives-ouvertes.fr/

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