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VOL. 67 | 2015 Existence and uniqueness for planar anisotropic and crystalline curvature flow
Antonin Chambolle, Matteo Novaga

Editor(s) Luigi Ambrosio, Yoshikazu Giga, Piotr Rybka, Yoshihiro Tonegawa

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.

Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1362.53073
MathSciNet: MR3587448

Digital Object Identifier: 10.2969/aspm/06710087

Subjects:
Primary: 53C44, 74E10, 74N05
Secondary: 35K55

Rights: Copyright © 2015 Mathematical Society of Japan

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