# Existence and uniqueness for planar anisotropic and crystalline curvature flow

created by novaga on 07 Feb 2013
modified on 31 Dec 2015

[BibTeX]

Published Paper

Inserted: 7 feb 2013
Last Updated: 31 dec 2015

Journal: Advanced Studies in Pure Mathematics
Volume: 67
Pages: 87-113
Year: 2015

Abstract:

We prove short-time existence of $\varphi$-regular solutions to the planar anisotropic curvature flow, including the crystalline case, with an additional forcing term possibly unbounded and discontinuous in time, such as for instance a white noise. We also prove uniqueness of such solutions when the anisotropy is smooth and elliptic. The main tools are the use of an implicit variational scheme in order to define the evolution, and the approximation with flows corresponding to regular anisotropies.