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

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

2011-03-17

arxiv.org/abs/1103.3365v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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

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