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- W2035854204 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. On introduit une nouvelle notion de solutions de viscosité pour une classe très singulière de problèmes non linéaires paraboliques sous forme non divergence dans un domaine périodique de dimension arbitraire, dont la diffusion sur les parties plates à pente nulle est si forte qu'elle devient une quantité non locale. Les problèmes incluent le flot de la variation et le mouvement d'une surface par une courbure moyenne cristalline. On établit un principe de comparaison, la stabilité par approximation par des problèmes régularisés paraboliques, et un théorème d'existence pour des données initiales continues génerales." @default.
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- W2035854204 title "Periodic total variation flow of non-divergence type in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>" @default.
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- W2035854204 doi "https://doi.org/10.1016/j.matpur.2013.11.007" @default.
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