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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the isoperimetric inequality
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by Jani Onninen PDF
Proc. Amer. Math. Soc. 131 (2003), 3821-3825 Request permission

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
  • MR Author ID: 679509
  • Email: jaonnine@maths.jyu.fi, jonninen@umich.edu
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 3821-3825
  • MSC (2000): Primary 26D10
  • DOI: https://doi.org/10.1090/S0002-9939-03-06998-3
  • MathSciNet review: 1999929