Global higher integrability of Jacobians on bounded domains

✍ Scribed by Jeff Hogan; Chun Li; Alan McIntosh; Kewei Zhang

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 177 KB
• Volume: 17
• Category: Article
• ISSN: 0294-1449
• DOI: 10.1016/s0294-1449(00)00108-6

✦ Synopsis

We give conditions for a vector-valued function u ∈ W 1,n (Ω, R n ), satisfying det Du(x) 0 on a bounded domain Ω, which imply that det Du(x) is globally higher integrable on Ω. We also give conditions for u ∈ W 1,n (Ω, R n ) such that det Du belongs to the Hardy space h 1 z (Ω) and exhibit some examples which show that our conditions are in some sense optimal. Applications to the weak convergence of Jacobians follow. Div-curl type extensions of these results to forms are also considered.