| Issue |
ESAIM: COCV
Volume 21, Number 2, April-June 2015
|
|
|---|---|---|
| Page(s) | 348 - 358 | |
| DOI | https://doi.org/10.1051/cocv/2014018 | |
| Published online | 17 October 2014 | |
Shape derivative of the Cheeger constant
1 LATP, Aix-Marseille
Université, 39 rue Joliot
Curie, 13453
Marseille cedex 13,
France.
enea.parini@univ-amu.fr
2 Instituto de Ciencias, University
Nac. Gral Sarmiento, J. M.
Gutierrez 1150, C.P.
1613
Los Polvorines Pcia de Bs. As,
Argentina
3 Dpto Matemática, FCEyN, University de
Buenos Aires, Ciudad Universitaria, Pabellón I (1428)
Buenos Aires,
Argentina.
nsaintie@dm.uba.ar; nsaintie@ungs.edu.ar
Received:
28
November
2013
Revised:
6
March
2014
This paper deals with the existence of the shape derivative of the Cheeger constant h1(Ω) of a bounded domain Ω. We prove that if Ω admits a unique Cheeger set, then the shape derivative of h1(Ω) exists, and we provide an explicit formula. A counter-example shows that the shape derivative may not exist without the uniqueness assumption.
Mathematics Subject Classification: 49Q10 / 49Q20
Key words: Shape derivative / CHEEGER constant / 1-Laplacian
© EDP Sciences, SMAI 2014
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