$(BV,L^p)$-decomposition, $p=1,2$, of Functions in Metric Random Walk Spaces

J. M. Mazon; M. Solera; J. Toledo

doi:10.1515/acv-2020-0011

paper

$(B V, L^{p})$ -decomposition, $p = 1, 2$ , of Functions in Metric Random Walk Spaces

arXiv:1907.10650 · doi:10.1515/acv-2020-0011

Abstract

In this paper we study the $(B V, L^{p})$ -decomposition, $p = 1, 2$ , of functions in metric random walk spaces, a general workspace that includes weighted graphs and nonlocal models used in image processing. We obtain the Euler-Lagrange equations of the corresponding variational problems and their gradient flows. In the case $p = 1$ we also study the associated geometric problem and the thresholding parameters.

arXiv admin note: text overlap with arXiv:1905.01130

(BV,Lp)-decomposition, p=1,2, of Functions in Metric Random Walk Spaces

Abstract

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$(B V, L^{p})$ -decomposition, $p = 1, 2$ , of Functions in Metric Random Walk Spaces