In this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set , different from a ball, which minimizes the ratio , where is the isoperimetric deficit and the Fraenkel asymmetry, giving a new proof of the quantitative isoperimetric inequality. Some new properties of the optimal set are also shown.
Accepté le :
DOI : 10.1051/cocv/2016002
Keywords: Isoperimetric inequality, quantitative isoperimetric inequality, isoperimetric deficit, Fraenkel asymmetry, rearrangement, shape derivative, optimality conditions
Bianchini, Chiara 1 ; Croce, Gisella 2 ; Henrot, Antoine 3
@article{COCV_2017__23_2_517_0,
author = {Bianchini, Chiara and Croce, Gisella and Henrot, Antoine},
title = {On the quantitative isoperimetric inequality in the plane},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {517--549},
year = {2017},
publisher = {EDP Sciences},
volume = {23},
number = {2},
doi = {10.1051/cocv/2016002},
zbl = {1456.49034},
mrnumber = {3608092},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016002/}
}
TY - JOUR AU - Bianchini, Chiara AU - Croce, Gisella AU - Henrot, Antoine TI - On the quantitative isoperimetric inequality in the plane JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 517 EP - 549 VL - 23 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016002/ DO - 10.1051/cocv/2016002 LA - en ID - COCV_2017__23_2_517_0 ER -
%0 Journal Article %A Bianchini, Chiara %A Croce, Gisella %A Henrot, Antoine %T On the quantitative isoperimetric inequality in the plane %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 517-549 %V 23 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016002/ %R 10.1051/cocv/2016002 %G en %F COCV_2017__23_2_517_0
Bianchini, Chiara; Croce, Gisella; Henrot, Antoine. On the quantitative isoperimetric inequality in the plane. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 517-549. doi: 10.1051/cocv/2016002
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