## Advanced Studies in Pure Mathematics

### Existence and uniqueness for planar anisotropic and crystalline curvature flow

#### 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.

#### Article information

Dates
Revised: 21 June 2013
First available in Project Euclid: 19 October 2018

https://projecteuclid.org/ euclid.aspm/1539916034

Digital Object Identifier
doi:10.2969/aspm/06710087

Mathematical Reviews number (MathSciNet)
MR3587448

Zentralblatt MATH identifier
1362.53073

#### Citation

Chambolle, Antonin; Novaga, Matteo. Existence and uniqueness for planar anisotropic and crystalline curvature flow. Variational Methods for Evolving Objects, 87--113, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710087. https://projecteuclid.org/euclid.aspm/1539916034