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.
Accepted:
DOI: 10.1051/cocv/2016002
Keywords: Isoperimetric inequality, quantitative isoperimetric inequality, isoperimetric deficit, Fraenkel asymmetry, rearrangement, shape derivative, optimality conditions
@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}, publisher = {EDP-Sciences}, volume = {23}, number = {2}, year = {2017}, doi = {10.1051/cocv/2016002}, zbl = {1456.49034}, mrnumber = {3608092}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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, Volume 23 (2017) no. 2, pp. 517-549. doi : 10.1051/cocv/2016002. http://archive.numdam.org/articles/10.1051/cocv/2016002/
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