Optimal constants for a nonlocal approximation of Sobolev norms and total variation

DOI10.2140/apde.2020.13.595zbMath1435.26008arXiv1708.01231OpenAlexW2742701900MaRDI QIDQ2307519

Nicola Picenni, Matteo Migliorini, Clara Antonucci, Massimo Gobbino

Publication date: 24 March 2020

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.01231

zbMATH Keywords

Sobolev spacesgamma-convergencemonotone rearrangementnonconvex functionalbounded-variation functionsnonlocal functional

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (4)

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics~II ⋮ On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics. I ⋮ Γ-convergence of non-local, non-convex functionals in one dimension

Cites Work

• Estimates for the topological degree and related topics
• Non-convex, non-local functionals converging to the total variation
• A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
• \(\Gamma\)-convergence, Sobolev norms, and BV functions
• On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation
• Non-local functionals related to the total variation and connections with image processing
• On the gap between the gamma-limit and the pointwise limit for a nonlocal approximation of the total variation
• Monotonicity of certain functionals under rearrangement
• New approximations of the total variation and filters in imaging
• \(\Gamma \)-convergence and Sobolev norms
• Further characterizations of Sobolev spaces
• Some new characterizations of Sobolev spaces
• A new characterization of Sobolev spaces
• Rearrangements of incidence tables
• Finite-difference approximation of free-discontinuity problems
• Lifting, degree, and distributional Jacobian revisited
• Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations

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