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VOL. 41 | 2003 Jacobians on Lipschitz domains of $\mathbbR^2$


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.


Published: 1 January 2003
First available in Project Euclid: 18 November 2014

zbMATH: 1151.42307
MathSciNet: MR1994518

Rights: Copyright © 2003, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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