On the gap between the gamma-limit and the pointwise limit for a nonlocal approximation of the total variation
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Publication:2174112
DOI10.2140/apde.2020.13.627zbMath1444.49008arXiv1712.04413OpenAlexW3098290291MaRDI QIDQ2174112
Clara Antonucci, Massimo Gobbino, Nicola Picenni
Publication date: 17 April 2020
Published in: Analysis \& PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.04413
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods involving semicontinuity and convergence; relaxation (49J45) 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 ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics. I ⋮ Γ-convergence of non-local, non-convex functionals in one dimension ⋮ Optimal constants for a nonlocal approximation of Sobolev norms and total variation
Cites Work
- Non-convex, non-local functionals converging to the total variation
- \(\Gamma\)-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
- Monotonicity of certain functionals under rearrangement
- Non-local, non-convex functionals converging to Sobolev norms
- 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
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