Existence and uniqueness for planar anisotropic and crystalline curvature flow
Existence and uniqueness for planar anisotropic and crystalline curvature flow
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DOI：
10.2969/aspm/06710087
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发表时间：
2013-02
期刊：
影响因子：
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通讯作者：
A. Chambolle;M. Novaga
中科院分区：
文献类型：
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作者：
A. Chambolle;M. Novaga
我们证明了平面各向异性曲率流（包括结晶情况）的 正则解的短时存在性，并且附加的强迫项可能在时间上无界且不连续，例如白噪声。当各向异性是光滑和椭圆时，我们还证明了此类解的唯一性。主要工具是使用隐式变分方案来定义演化，以及与规则各向异性相对应的流的近似。
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.