Some isoperimetric inequalities with application to the Stekloff problem

Antoine Henrot (1) , Gérard A. Philippin (2) , Abdesselam Safoui (3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 ULaval - Université Laval [Québec]
3 Département de Mathématiques [Marrakech]

In this paper we establish isoperimetric inequalities for the product of some moments of inertia. As an application, we obtain an isoperimetric inequality for the product of the $N$ first nonzero eigenvalues of the Stekloff problem in $\mathbb{R}^N$.

Mots clés: Moments of inertia; Stekloff eigenvalues; isoperimetric inequalities

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Antoine Henrot, Gérard A. Philippin, Abdesselam Safoui. Some isoperimetric inequalities with application to the Stekloff problem. Journal of Convex Analysis, 2008, 15 (3), pp.581-592. ⟨hal-00267931⟩