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• W2964307381 abstract "We present new results concerning the approximation of the total variation, $$int _{Omega } |nabla u|$$ , of a function u by non-local, non-convex functionals of the form $$begin{aligned} Lambda _delta (u) = int _{Omega } int _{Omega } frac{delta varphi big ( |u(x) - u(y)|/ delta big )}{|x - y|^{d+1}} , dx , dy, end{aligned}$$ as $$delta rightarrow 0$$ , where $$Omega $$ is a domain in $$mathbb {R}^d$$ and $$varphi : [0, + infty ) rightarrow [0, + infty )$$ is a non-decreasing function satisfying some appropriate conditions. The mode of convergence is extremely delicate and numerous problems remain open. De Giorgi’s concept of $$Gamma $$ -convergence illuminates the situation, but also introduces mysterious novelties. The original motivation of our work comes from Image Processing." @default.
• W2964307381 created "2019-07-30" @default.
• W2964307381 creator A5021854077 @default.
• W2964307381 creator A5078018452 @default.
• W2964307381 date "2018-01-24" @default.
• W2964307381 modified "2023-10-18" @default.
• W2964307381 title "Non-local Functionals Related to the Total Variation and Connections with Image Processing" @default.
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• W2964307381 doi "https://doi.org/10.1007/s40818-018-0044-1" @default.
• W2964307381 hasPublicationYear "2018" @default.
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