Characterizations of the Sobolev norms and the total variation via nonlocal functionals, and related problems

2025/07/01 by Nguyen, Hoai-Minh · 1 citation
#26B15 #26B25 #26B30 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.00842

Abstract

We briefly discuss the contribution of Haïm Brezis and his co-authors on the characterizations of the Sobolev norms and the total variation using non-local functionals. Some ideas of the analysis are given and new results are presented.

Citations

• Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms
• Some remarks on a formula for Sobolev norms due to Brezis, Van\n Schaftingen and Yung
• Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung
• New Brezis-Van Schaftingen-Yung Sobolev type inequalities connected with maximal inequalities and one parameter families of operators
• Γ-convergence of non-local, non-convex functionals in one dimension
• On Hardy and Caffarelli-Kohn-Nirenberg inequalities
• On anisotropic Sobolev spaces
• A refined estimate for the topological degree
• New characterizations of magnetic Sobolev spaces
• Magnetic BV functions and the Bourgain-Brezis-Mironescu formula
• Non-local functionals related to the total variation and connections with Image Processing
• The BBM formula revisited
• On functions of bounded mean oscillation

Cited by

• Characterisations of Sobolev spaces and constant functions over metric spaces

Related

• A sharp lower bound for a class of non-local approximations of the total variation
• On the shape factor of interaction laws for a non-local approximation of\n the Sobolev norm and the total variation
• Non-local functionals, total variation, and Gamma-convergence with respect to area-strict convergence
• BV functions and nonlocal functionals in metric measure spaces
• Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms