Advanced Studies in Pure Mathematics

Existence and uniqueness for planar anisotropic and crystalline curvature flow

Antonin Chambolle and Matteo Novaga

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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

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

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

Permanent link to this document euclid.aspm/1539916034

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Anisotropy implicit variational scheme geometric evolutions crystal growth


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.

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