This paper deals with the existence of the shape derivative of the Cheeger constant of a bounded domain . We prove that if admits a unique Cheeger set, then the shape derivative of exists, and we provide an explicit formula. A counter-example shows that the shape derivative may not exist without the uniqueness assumption.
DOI: 10.1051/cocv/2014018
Keywords: Shape derivative, CHEEGER constant, 1-Laplacian
@article{COCV_2015__21_2_348_0, author = {Parini, Enea and Saintier, Nicolas}, title = {Shape derivative of the {Cheeger} constant}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {348--358}, publisher = {EDP-Sciences}, volume = {21}, number = {2}, year = {2015}, doi = {10.1051/cocv/2014018}, mrnumber = {3348401}, zbl = {1315.49018}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014018/} }
TY - JOUR AU - Parini, Enea AU - Saintier, Nicolas TI - Shape derivative of the Cheeger constant JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 348 EP - 358 VL - 21 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014018/ DO - 10.1051/cocv/2014018 LA - en ID - COCV_2015__21_2_348_0 ER -
%0 Journal Article %A Parini, Enea %A Saintier, Nicolas %T Shape derivative of the Cheeger constant %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 348-358 %V 21 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014018/ %R 10.1051/cocv/2014018 %G en %F COCV_2015__21_2_348_0
Parini, Enea; Saintier, Nicolas. Shape derivative of the Cheeger constant. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 2, pp. 348-358. doi : 10.1051/cocv/2014018. http://archive.numdam.org/articles/10.1051/cocv/2014018/
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