Calculus of Variations and Geometric Measure Theory
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A. Chambolle - M. Novaga

Existence and uniqueness for planar anisotropic and crystalline curvature flow

created by novaga on 07 Feb 2013
modified on 02 Jan 2018


Published Paper

Inserted: 7 feb 2013
Last Updated: 2 jan 2018

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

ArXiv: 1302.2216 PDF


We prove short-time existence of \phi-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.


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