Calculus of Variations and Geometric Measure Theory
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L. Briani - G. Buttazzo - F. Prinari

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

created by prinari on 19 May 2021


Submitted Paper

Inserted: 19 may 2021
Last Updated: 19 may 2021

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


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