Sobolev spaces revisited

DOI10.4171/RLM/976MaRDI QIDQ2083988

Jean Van Schaftingen, Po-Lam Yung, Andreas Seeger, Haim Brezis

Publication date: 17 October 2022

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.01410

zbMATH Keywords

Sobolev spacesbounded variationBBM formulaGagliardo seminormsGagliardo-Nirenberg interpolation

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (9)

Poincaré inequality meets Brezis-Van Schaftingen-Yung formula on metric measure spaces ⋮ Generalized Brezis-Seeger-Van Schaftingen-Yung formulae and their applications in ball Banach Sobolev spaces ⋮ Brezis-van Schaftingen-Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo-Nirenberg inequalities ⋮ 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 ⋮ Gagliardo representation of norms of ball quasi-Banach function spaces ⋮ The Bourgain-Brezis-Mironescu formula on ball Banach function spaces ⋮ New Brezis-van Schaftingen-Yung-Sobolev type inequalities connected with maximal inequalities and one parameter families of operators ⋮ Spaces of Besov-Sobolev type and a problem on nonlinear approximation

Cites Work

• A new formula for the \(L^p\) norm
• Harmonic analysis of the space BV.
• Gagliardo-Nirenberg inequalities and non-inequalities: the full story
• Non-local functionals related to the total variation and connections with image processing
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail
• Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung
• Some new characterizations of Sobolev spaces
• An embedding theorem for BV-functions
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