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arXiv · 1302.0618

Periodic total variation flow of non-divergence type in Rn

Mi-Ho Giga·Yoshikazu Giga·Norbert Pozar
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Abstract

We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a crystalline mean curvature. We establish a comparison principle, the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data.

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Mi-Ho Giga, Yoshikazu Giga, Norbert Pozar. 2013-02-04. Periodic total variation flow of non-divergence type in Rn. https://arxiv.org/abs/1302.0618

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