We consider the problem of minimizing or maximizing the quantity λ (Ω) T q (Ω) on the class
of open sets of prescribed Lebesgue measure. Here q> 0 is fixed, λ (Ω) denotes the first …

We prove a comparison principle for positive supersolutions and subsolutions to the Lane–
Emden equation for the p-Laplacian, with subhomogeneous power in the right-hand side …

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 …

In this paper, we study optimal lower and upper bounds for functionals involving the first
Dirichlet eigenvalue λ F⁢(p, Ω) of the anisotropic p-Laplacian, 1< p<+∞. Our aim is to …

We provide a sharp double-sided estimate for Poincaré–Sobolev constants on a convex set,
in terms of its inradius and NN-dimensional measure. Our results extend and unify previous …

In this paper we investigate upper and lower bounds of two shape functionals involving the
maximum of the torsion function. More precisely, we consider T (Ω)/(M (Ω) 1Ω1) and M (Ω) λ1 …

For domains in $\mathbb {R}^ d $, $ d\geq 2$, we prove universal upper and lower bounds
on the product of the bottom of the spectrum for the Laplacian to the power $ p> 0$ and the …

In this paper we study extremal behaviors of the mean to max ratio of the p-torsion function
with respect to the geometry of the domain. For p larger than the dimension of the space N …

The aim of this paper is to obtain optimal estimates for the first Robin eigenvalue of the
anisotropic p-Laplace operator, namely: λ 1 (β, Ω)= min ψ∈ W 1, p (Ω)∖{0}⁡∫ Ω F (∇ ψ) pd …

We consider the torsion function for the Dirichlet Laplacian− Δ, and for the Schrödinger
operator− Δ+ V on an open set Ω⊂ ℝ m of finite Lebesgue measure 0<| Ω|<∞ with a real …