Some remarks on a formula for Sobolev norms due to Brezis, Van\n Schaftingen and Yung

2021/01/31 by Arkady Poliakovsky, Poliakovsky, Arkady · 2 citations
Social Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Military, Security, and Education Studies

paper · pdf · doi:10.48550/arxiv.2102.00557

openalex publication_date 2021/01/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We provide answers to some questions raised in a recent work by H. Brezis, J.\nVan Schaftingen and Po-Lam Yung concerning the Gagliardo semi-norm\n|u|_W^s,q computed at s = 1, when the strong L^q is replaced by weak\nL^q. In particular, we address generalization of their results for a general\ndomain and non-smooth functions.\n

Cited by

• Characterizations of the Sobolev norms and the total variation via nonlocal functionals, and related problems
• Sharp Brezis--Seeger--Van Schaftingen--Yung Formulae for Higher-Order Gradients in Ball Banach Function Spaces

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