Anisotropic total variation flow of non-divergence type on a higher\n dimensional torus

2013/05/25 by Mi-Ho Giga, Yoshikazu Giga, Giga, Mi-Ho +3
Computer Science · Mathematics · #35B51 #35D40 #35K55 #35K67 #35K93 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1305.5904

openalex publication_date 2013/05/25 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

We extend the theory of viscosity solutions to a class of very singular\nnonlinear parabolic problems of non-divergence form in a periodic domain of an\narbitrary dimension with diffusion given by an anisotropic total variation\nenergy. We give a proof of a comparison principle, an outline of a proof of the\nstability under approximation by regularized parabolic problems, and an\nexistence theorem for general continuous initial data, which extend the results\nrecently obtained by the authors.\n

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