## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- 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

### Jacobians on Lipschitz domains of $\mathbbR^2$

#### 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

**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