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Comptes Rendus Mathématique
Volume 353, n° 7
pages 589-593 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.006
Received : 29 November 2014 ;  accepted : 13 April 2015
An analytic proof of the planar quantitative isoperimetric inequality
Une démonstration analytique de l'inégalité isopérimétrique quantitative dans le plan

Guohua Li a , Xinyu Zhao a , Zongqi Ding a , Renjin Jiang a, b
a School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875 Beijing, People's Republic of China 
b Department of Mathematics, University Autònoma Barcelona, 08193 Bellaterra (Barcelona), Spain 


We give an analytic proof of the quantitative isoperimetric inequality in the plane and give an estimation of the upper bound of the constant via maximizing the  -norm of the gradient of solutions to the Poisson equation.

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On donne une démonstration analytique de l'inégalité isopérimétrique quantitative dans le plan, et on établit une estimation de la borne supérieure de la constante en maximisant la norme   du gradient de la solution de l'équation de Poisson.

The full text of this article is available in PDF format.

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