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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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An optimal Poincaré inequality in $L^1$ for convex domains
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by Gabriel Acosta and Ricardo G. Durán PDF
Proc. Amer. Math. Soc. 132 (2004), 195-202 Request permission

Abstract:

For convex domains $\Omega \subset \mathbb {R}^n$ with diameter $d$ we prove \[ \|u\|_{L^1(\omega )} \le \frac {d}{2} \|\nabla u\|_{L^1(\omega )} \] for any $u$ with zero mean value on $\omega$. We also show that the constant $1/2$ in this inequality is optimal.
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Additional Information
  • Gabriel Acosta
  • Affiliation: Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina
  • Email: gacosta@ungs.edu.ar
  • Ricardo G. Durán
  • Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
  • ORCID: 0000-0003-1349-3708
  • Email: rduran@dm.uba.ar
  • Received by editor(s): May 10, 2002
  • Received by editor(s) in revised form: September 10, 2002
  • Published electronically: April 24, 2003
  • Additional Notes: This work was supported by Universidad de Buenos Aires under grant TX048, ANPCyT under grant PICT 03-05009 and by CONICET under grant PIP 0660/98. The second author is a member of CONICET, Argentina
  • Communicated by: Andreas Seeger
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 195-202
  • MSC (2000): Primary 26D10
  • DOI: https://doi.org/10.1090/S0002-9939-03-07004-7
  • MathSciNet review: 2021262