Calculus of Variations and Geometric Measure Theory

D. Bucur - V. Ferone - C. Nitsch - C. Trombetti

Weinstock inequality in higher dimensions

created by bucur on 13 Oct 2017


Submitted Paper

Inserted: 13 oct 2017
Last Updated: 13 oct 2017

Year: 2017

ArXiv: 1710.04587 PDF


We prove that the Weinstock inequality for the first nonzero Steklov eigenvalue holds in $\R^n$, for $n\ge 3$, in the class of convex sets with prescribed surface area. The key result is a sharp isoperimetric inequality involving simultanously the surface area, the volume and the boundary momentum of convex sets. As a by product, we also obtain some isoperimetric inequalities for the first Wentzell eigenvalue.