Proceedings of the Centre for Mathematics and its Applications

Jacobians on Lipschitz domains of $\mathbbR^2$

Zengjian Lou

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Abstract

In this note we prove estimates of Jacobian determinants of $Du$ on strongly Lipschitz domains $\Omega$ in $\mathbbR^2$. The theorem consists of two parts: one is an estimate in terms of the $BMO_r(\Omega)$ norm for $u$ in the Sobolev space $W^{1,2}(\Omega,\mathbbR^@)$ with boundary zero, and another is an estimate in terms of the $BMO_z(\omega)$ norm for $u$ in $W^{1,2}(\Omega,\mathbbR^2)$ with no boundary conditions.

Article information

Source
International Conference on Harmonic Analysis and Related Topics. Xuan Thinh Duong and Alan Pryde, eds. Proceedings of the Centre for Mathematics and its Applications, v. 41. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2003), 96-109

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416322430

Mathematical Reviews number (MathSciNet)
MR1994518

Zentralblatt MATH identifier
1151.42307

Citation

Lou, Zengjian. Jacobians on Lipschitz domains of $\mathbbR^2$. International Conference on Harmonic Analysis and Related Topics, 96--109, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2003. https://projecteuclid.org/euclid.pcma/1416322430


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