Calculus of Variations and Geometric Measure Theory

L. Briani - G. Buttazzo - F. Prinari

Inequalities between torsional rigidity and principal eigenvalue of the $p$-Laplacian

created by prinari on 19 May 2021
modified on 19 Nov 2021


Accepted Paper

Inserted: 19 may 2021
Last Updated: 19 nov 2021

Journal: Calc. Var. Partial Differ. Equ.
Year: 2021


We consider the torsional rigidity and the principal eigenvalue related to the $p$-Laplace operator. The goal is to find upper and lower bounds to products of suitable powers of the quantities above in various classes of domains. The limit cases $p=1$ and $p=\infty$ are also analyzed, which amount to consider the Cheeger constant of a domain and functionals involving the distance function from the boundary.

Keywords: shape optimization, Torsional rigidity, Convex domains, principal eigenvalue, Cheeger constant