Passing to the limit in maximal slope curves: from a regularized\n Perona-Malik equation to the total variation flow

2011/03/17 by Maria Colombo, Massimo Gobbino, Colombo, Maria +1 · 1 citation
Mathematics · #35B40 #35K55 #35K90 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1103.3365

openalex publication_date 2011/03/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove that solutions of a mildly regularized Perona-Malik equation\nconverge, in a slow time scale, to solutions of the total variation flow. The\nconvergence result is global-in-time, and holds true in any space dimension.\nThe proof is based on the general principle that "the limit of gradient-flows\nis the gradient-flow of the limit". To this end, we exploit a general result\nrelating the Gamma-limit of a sequence of functionals to the limit of the\ncorresponding maximal slope curves.\n

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• Metric gradient flows and variational principles

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