平面各向异性和晶体曲率流的存在唯一性
Existence and uniqueness for planar anisotropic and crystalline curvature flow
AI总结：
本文通过隐式变分方案和正则各向异性逼近，证明了平面各向异性曲率流（包括晶体情况）在时间上可能无界不连续强迫项（如白噪声）下的ϕ-正则解的短时存在性，以及光滑椭圆各向异性情形下解的唯一性。
摘要：
我们证明了平面各向异性曲率流（包括晶体情况）的ϕ-正则解的短时存在性，其中包含可能无界且时间上不连续的附加强迫项，例如白噪声。我们还证明了当各向异性光滑且椭圆时此类解的唯一性。主要工具是使用隐式变分方案来定义演化，以及用对应于正则各向异性的流进行逼近。
英文摘要：
We prove short-time existence of ϕ-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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
