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Double logarithmic inequality with a sharp constant

Authors: S. Ibrahim, M. Majdoub and N. Masmoudi
Journal: Proc. Amer. Math. Soc. 135 (2007), 87-97
MSC (2000): Primary 49K20, 35L70
Published electronically: June 13, 2006
MathSciNet review: 2280178
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Abstract: We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log estimate is ``almost'' sharp. These estimates are applied to prove a Moser-Trudinger type inequality for solutions of a 2D wave equation.

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S. Ibrahim
Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4L8

M. Majdoub
Affiliation: Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire 1060, Tunis, Tunisia

N. Masmoudi
Affiliation: Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012

Received by editor(s): January 9, 2005
Received by editor(s) in revised form: July 13, 2005
Published electronically: June 13, 2006
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2006 American Mathematical Society

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