Volume 21, Number 2, April-June 2015
|Page(s)||348 - 358|
|Published online||17 October 2014|
Shape derivative of the Cheeger constant
1 LATP, Aix-Marseille
Université, 39 rue Joliot
Marseille cedex 13,
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.
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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