Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-22T16:48:34.689Z Has data issue: false hasContentIssue false
  • English
  • Français

Div-curl type theorems on Lipschitz domains

Published online by Cambridge University Press:  17 April 2009

Zengjian Lou
Zengjian Lou
Affiliation:
Department of Mathematics, Shantou University, Shantou, Guangdong 515063, Peoples Repbulic of China, e-mail: zjlou@stu.edu.cn
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For Lipschitz domains of ℝn we prove div-curl type theorems, which are extensions to domains of the Div-Curl Theorem on ℝn by Coifman, Lions, Meyer and Semmes. Applying the div-curl type theorems we give decompositions of Hardy spaces on domains.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 31 - 38
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Adams, R.A., Sobolev spaces (Academic Press, New York, 1975).Google Scholar
[2]Chang, D.C., ‘The dual of Hardy spaces on a domain in ℝn’, Forum Math. 6 (1994), 65–81.CrossRefGoogle Scholar
[3]Chang, D.C., Dafni, G. and Sadosky, C., ‘A div-curl lemma in BMO on a domain’ (to appear).Google Scholar
[4]Chang, D.C., Krantz, S.G. and Stein, E.M., ‘ℋp theory on a smooth domain in ℝn and elliptic boundary value problems’, J. Funct. Anal. 114 (1993), 286–347.CrossRefGoogle Scholar
[5]Coifman, R., Lions, P.L., Meyer, Y. and Semmes, S., ‘Compensated compactness and Hardy spaces’, J. Math. Pures Appl. 72 (1993), 247–286.Google Scholar
[6]Jones, P.W., ‘Extension theorems for BMO’, Indiana Univ. Math. J. 29 (1980), 41–66.CrossRefGoogle Scholar
[7]Lou, Z., ‘Jacobian on Lipsctitz domains of ℝ2’, Proc. Centre Math. Appl. Austral. Nat. Univ. 41 (2003), 96–109.Google Scholar
[8]Lou, Z. and McIntosh, A., ‘Hardy spaces of exact forms on ℝn’, Trans. Amer. Math. Soc. 357 (2005), 1469–1496.CrossRefGoogle Scholar
[9]Lou, Z. and McIntosh, A., ‘Hardy spaces of exact forms on Lipschitz domains in ℝn’, Indiana Univ. Math. J. 54 (2004), 581–609.Google Scholar
[10]Nečas, J., Les méthodes directes en théorie des équations elliptiques, (et Cie Paris, Masson, Editors) (Academia, Editeurs, Prague, 1967).Google Scholar