The Div-Curl Lemma Revisited

2007/12/13 by Dan Poliševski, Polisevski, Dan
Computer Science · Engineering · Mathematics · #46E40 #47B07 #49J45 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0712.2133

openalex publication_date 2007/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Div-Curl Lemma, which is the basic result of the compensated compactness theory in Sobolev spaces, was introduced by F. Murat (1978) with distinct proofs for the L²(Ω) and L^p(Ω), p ≠ 2, cases. In this note we present a slightly different proof, relying only on a Green-Gauss integral formula and on the usual Rellich-Kondrachov compactness properties.

Related

• A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces
• A Functional Analytic Perspective to the div-curl Lemma
• Endpoint for the div-curl lemma in Hardy spaces
• A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains
• Compactness estimates for the ∂ - Neumann problem in weighted L² - spaces