Viscosity solutions for a polymer crystal growth model Pierre CardaliaguetOlivier LeyAurelien Monteillet 49L2535F2535A0535D0535B5045G10nonlocal Hamilton-Jacobi equationsnonlocal front propagationlevel-set approachgeometrical propertieslower-bound gradient estimateviscosity solutionseikonal equationheat equation 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. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4322 10.1512/iumj.2011.60.4322 en Indiana Univ. Math. J. 60 (2011) 895 - 936 state-of-the-art mathematics http://iumj.org/access/