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

2021/05/19 by Luca Briani, Luca, Briani, Buttazzo Giuseppe +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2105.09353

openalex publication_date 2021/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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=∞ are also analyzed, which amount to consider the Cheeger constant of a domain and functionals involving the distance function from the boundary.

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