Advanced Studies in Pure Mathematics

Existence and uniqueness for planar anisotropic and crystalline curvature flow

Antonin Chambolle and Matteo Novaga

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Source
Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 87-113

Dates
Received: 8 February 2013
Revised: 21 June 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916034

Digital Object Identifier
doi:10.2969/aspm/06710087

Mathematical Reviews number (MathSciNet)
MR3587448

Zentralblatt MATH identifier
1362.53073

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 74N05: Crystals 74E10: Anisotropy
Secondary: 35K55: Nonlinear parabolic equations

Keywords
Anisotropy implicit variational scheme geometric evolutions crystal growth

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


Export citation