Geodesic
Symmetry breaking in a constrained Cheeger type isoperimetric inequality
Brandolini, Barbara1 ; Della Pietra, Francesco1 ; Nitsch, Carlo1 ; Trombetti, Cristina1
1 Universitàdegli Studi di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Complesso Monte S. Angelo - Via Cintia, 80126 Napoli, Italia.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 359-371

Voir la notice de l'article provenant de la source Numdam

The study of the optimal constant 𝒦q(Ω) in the Sobolev inequality ||u||Lq(Ω)≤1/𝒦q(Ω)||Du||(ℝn), 1≤q<1*, for BV functions which are zero outside Ω and with zero mean value inside Ω, leads to the definition of a Cheeger type constant. We are interested in finding the best possible embedding constant in terms of the measure of Ω alone. We set up an optimal shape problem and we completely characterize, on varying the exponent q, the behaviour of optimal domains. Among other things we establish the existence of a threshold value 1≤q̅<1* above which the symmetry of optimal domains is broken. Several differences between the cases n=2 and n≥3 are emphasized.

Reçu le :
DOI : 10.1051/cocv/2014016
Classification : 49Q20, 39B05
Keywords: Cheeger inequality, optimal shape, symmetry and asymmetry

Brandolini, Barbara 1 ; Della Pietra, Francesco 1 ; Nitsch, Carlo 1 ; Trombetti, Cristina 1

1 Universitàdegli Studi di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Complesso Monte S. Angelo - Via Cintia, 80126 Napoli, Italia. 
@article{COCV_2015__21_2_359_0,
     author = {Brandolini, Barbara and Della Pietra, Francesco and Nitsch, Carlo and Trombetti, Cristina},
     title = {Symmetry breaking in a constrained {Cheeger} type isoperimetric inequality},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {359--371},
     publisher = {EDP-Sciences},
     volume = {21},
     number = {2},
     year = {2015},
     doi = {10.1051/cocv/2014016},
     mrnumber = {3348402},
     zbl = {1319.49066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014016/}
}
TY  - JOUR
AU  - Brandolini, Barbara
AU  - Della Pietra, Francesco
AU  - Nitsch, Carlo
AU  - Trombetti, Cristina
TI  - Symmetry breaking in a constrained Cheeger type isoperimetric inequality
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2015
SP  - 359
EP  - 371
VL  - 21
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014016/
DO  - 10.1051/cocv/2014016
LA  - en
ID  - COCV_2015__21_2_359_0
ER  - 
%0 Journal Article
%A Brandolini, Barbara
%A Della Pietra, Francesco
%A Nitsch, Carlo
%A Trombetti, Cristina
%T Symmetry breaking in a constrained Cheeger type isoperimetric inequality
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2015
%P 359-371
%V 21
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014016/
%R 10.1051/cocv/2014016
%G en
%F COCV_2015__21_2_359_0
Brandolini, Barbara; Della Pietra, Francesco; Nitsch, Carlo; Trombetti, Cristina. Symmetry breaking in a constrained Cheeger type isoperimetric inequality. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 359-371. doi: 10.1051/cocv/2014016

Cité par Sources :