Mathematical analysis/Partial differential equations
An analytic proof of the planar quantitative isoperimetric inequality
[Une démonstration analytique de l'inégalité isopérimétrique quantitative dans le plan]

Présenté par : Haïm Brézis

Li, Guohua1 ; Zhao, Xinyu1 ; Ding, Zongqi1 ; Jiang, Renjin1, 2
1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875 Beijing, People's Republic of China
2 Department of Mathematics, University Autònoma Barcelona, 08193 Bellaterra (Barcelona), Spain
Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 589-593.

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 L∞ du gradient de la solution de l'équation de Poisson.

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 L∞-norm of the gradient of solutions to the Poisson equation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.04.006
Li, Guohua 1 ; Zhao, Xinyu 1 ; Ding, Zongqi 1 ; Jiang, Renjin 1, 2

1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875 Beijing, People's Republic of China
2 Department of Mathematics, University Autònoma Barcelona, 08193 Bellaterra (Barcelona), Spain 
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Li, Guohua; Zhao, Xinyu; Ding, Zongqi; Jiang, Renjin. An analytic proof of the planar quantitative isoperimetric inequality. Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 589-593. doi : 10.1016/j.crma.2015.04.006. http://archive.numdam.org/articles/10.1016/j.crma.2015.04.006/

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