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A note on the isoperimetric inequality

Author: Jani Onninen
Journal: Proc. Amer. Math. Soc. 131 (2003), 3821-3825
MSC (2000): Primary 26D10
Published electronically: June 18, 2003
MathSciNet review: 1999929
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the sharp integral form on the isoperimetric inequality holds for those orientation-preserving mappings $f\in W^\frac{n^2}{n+1}_{loc}(\Omega , \mathbb{R}^n)$ whose Jacobians obey the rule of integration by parts.

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Additional Information

Jani Onninen
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland
Address at time of publication: Department of Mathematics, University of Michigan, 525 E. University Ave., Ann Arbor, MI 48109-1109, USA

Received by editor(s): April 18, 2002
Received by editor(s) in revised form: July 23, 2002
Published electronically: June 18, 2003
Additional Notes: The author was supported in part by the Academy of Finland, project 39788, and by the foundations Magnus Ehrnroothin Säätiö and Vilho, Yrjö ja Kalle Väisälän Rahasto. This research was done when the author was visiting the University of Michigan. He thanks the Department of Mathematics for their hospitality
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2003 American Mathematical Society