A surprising formula for Sobolev norms-Reference-Cited by-同舟云学术

A surprising formula for Sobolev norms

Published:2021-02-16 Issue:8 Volume:118 Page:e2025254118
ISSN:0027-8424
Container-title:Proceedings of the National Academy of Sciences
language:en
Short-container-title:Proc Natl Acad Sci USA

Author:

Brezis Haïm,Van Schaftingen Jean^ORCID,Yung Po-Lam^ORCID

Abstract

We establish the equivalence between the Sobolev seminorm ‖∇u‖Lp and a quantity obtained when replacing strong Lp by weak Lp in the Gagliardo seminorm |u|Ws,p computed at s=1. As corollaries we derive alternative estimates in some exceptional cases (involving W1,1) where the “anticipated” fractional Sobolev and Gagliardo–Nirenberg inequalities fail.

Funder

Hong Kong Research Grant Council

Publisher

Proceedings of the National Academy of Sciences

Subject

Multidisciplinary

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