Lorenzo Carletti

activity

20242026

collaborators

4 papers

math.AP2026

A priori bounds for energy-bounded solutions of critical polyharmonic equations

Lorenzo Carletti, Bruno Premoselli

We investigate critical polyharmonic equations of the type: $Lu = ∣ u ∣^{2^{♯} - 2} u in Ω$ with Dirichlet boundary conditions, in a smooth bounded domain $Ω$ of $…

math.AP2025

Optimal Sobolev inequalities of high order with $L^{2}$ -remainder

Lorenzo Carletti, Frédéric Robert

We investigate the validity of the optimal higher-order Sobolev inequality $H_{k}^{2} (M^{n}) ↪ L^{\frac{2 n}{n - 2 k}} (M^{n})$ on a closed Riemannian manifold when the remainder t…

math.AP2024

Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis

Lorenzo Carletti

Let $(M, g)$ be a closed Riemannian manifold of dimension $n$ , and $k \geq 1$ an integer such that $n > 2 k$ . We show that there exists $B_{0} > 0$ such that for all $u \in H^{k} (M)$ , \[\|u…

math.AP2024

The Green's function of polyharmonic operators with diverging coefficients: Construction and sharp asymptotics

Lorenzo Carletti

We show existence, uniqueness and positivity for the Green's function of the operator $(Δ_{g} + α)^{k}$ in a closed Riemannian manifold $(M, g)$ , of dimension $n > 2 k$ , $k \in N$ ,…

A priori bounds for energy-bounded solutions of critical polyharmonic equations

Optimal Sobolev inequalities of high order with L2-remainder

Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis

The Green's function of polyharmonic operators with diverging coefficients: Construction and sharp asymptotics

Optimal Sobolev inequalities of high order with $L^{2}$ -remainder