Characterization of Sobolev and BV spaces
From MaRDI portal
Publication:647602
DOI10.1016/j.jfa.2011.07.018zbMath1236.46032OpenAlexW1963987355MaRDI QIDQ647602
Giovanni Leoni, Daniel E. Spector
Publication date: 24 November 2011
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2011.07.018
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 (42)
Two subtle convex nonlocal approximations of the BV-norm ⋮ On a generalization of \(L^p\)-differentiability ⋮ Analysis and Application of a Nonlocal Hessian ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics~II ⋮ Jump detection in Besov spaces via a new BBM formula. Applications to Aviles–Giga-type functionals ⋮ A class of high order nonlocal operators ⋮ Non-local functionals related to the total variation and connections with image processing ⋮ Existence of minimizers for a generalized liquid drop model with fractional perimeter ⋮ Asymptotic behaviours in fractional Orlicz-Sobolev spaces on Carnot groups ⋮ A restricted nonlocal operator bridging together the Laplacian and the fractional Laplacian ⋮ BMO-type seminorms from Escher-type tessellations ⋮ Generalized Brezis-Seeger-Van Schaftingen-Yung formulae and their applications in ball Banach Sobolev spaces ⋮ Yet another heat semigroup characterization of BV functions on Riemannian manifolds ⋮ Bourgain-Brezis-Mironescu convergence via Triebel-Lizorkin spaces ⋮ A remake of Bourgain-Brezis-Mironescu characterization of Sobolev spaces ⋮ The variational approach to \(s\)-fractional heat flows and the limit cases \(s \rightarrow 0^+\) and \(s \rightarrow 1^-\) ⋮ Characterization of generalized Orlicz spaces ⋮ Bourgain-Brezis-Mironescu formula for \(W^{s, p}_q\)-spaces in arbitrary domains ⋮ A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics. I ⋮ Gagliardo representation of norms of ball quasi-Banach function spaces ⋮ The Bourgain-Brezis-Mironescu formula on ball Banach function spaces ⋮ On the convergence rate of some nonlocal energies ⋮ Second order expansion for the nonlocal perimeter functional ⋮ A nonlocal Laplacian-based model for bituminous surfacing crack recovery and its MPI implementation ⋮ On limiting relations for capacities ⋮ A Bourgain–Brezis–Mironescu characterization of higher order Besov–Nikol^{\prime }skii spaces ⋮ Corrigendum to ``Characterization of Sobolev and \(BV\) spaces ⋮ New characterizations of Sobolev spaces on the Heisenberg group ⋮ Asymmetric anisotropic fractional Sobolev norms ⋮ Characterization of polynomials and higher-order Sobolev spaces in terms of functionals involving difference quotients ⋮ Localization of nonlocal gradients in various topologies ⋮ Estimates for the topological degree and related topics ⋮ The core-radius approach to supercritical fractional perimeters, curvatures and geometric flows ⋮ Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups ⋮ \(L^p\)-Taylor approximations characterize the Sobolev space \(W^{1,p}\) ⋮ Fractional Sobolev norms and BV functions on manifolds ⋮ On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces ⋮ Magnetic BV-functions and the Bourgain-Brezis-Mironescu formula ⋮ The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains ⋮ Characterizations of second order Sobolev spaces ⋮ A new variational characterization of Sobolev spaces
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlinear total variation based noise removal algorithms
- A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
- Gamma-convergence of nonlocal perimeter functionals
- Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
- On an open question about functions of bounded variation.
- An estimate in the spirit of Poincaré's inequality
- Limits of higher-order Besov spaces and sharp reiteration theorems
- Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
- On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
- \(\Gamma \)-convergence and Sobolev norms
- Further characterizations of Sobolev spaces
- Simple proofs of some results of Reshetnyak
- Nonlocal Operators with Applications to Image Processing
- Nonlocal Linear Image Regularization and Supervised Segmentation
- Can the Nonlocal Characterization of Sobolev Spaces by Bourgain et al. Be Useful for Solving Variational Problems?
- On Regularity of the Boundary in the Theory of Sobolev Spaces
- Notes on limits of Sobolev spaces and the continuity of interpolation scales
- The interplay between analysis and topology in some nonlinear PDE problems
- On limiting embeddings of Besov spaces
This page was built for publication: Characterization of Sobolev and BV spaces
