Shape derivative of the Cheeger constant
Enea Parini, Nicolas Saintier · ESAIM Control Optimisation and Calculus of Variations · 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.