Inequalities between torsional rigidity and principal eigenvalue of the p-Laplacian
Luca Briani, Giuseppe Buttazzo, Francesca Prinari · Calculus of Variations and Partial Differential Equations · 2022
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 $$p=1$$ p = 1 and $$p=\infty $$ p = ∞ are also analyzed, which amount to consider the Cheeger constant of a domain and functionals involving the distance function from the boundary.