Lorenzo D’Ambrosio

activity

20002025

most citedSome Liouville theorems for the fractional Laplacian

49 citations · 152 across the 11 of their papers we have counts for

collaborators

12 papers

math.AP2025

Characterization of positive superharmonic functions in a half-space

Lorenzo D'Ambrosio, Enzo Mitidieri

We prove a representation formula for superharmonic functions on the half-space $R_{+}^{N} := R^{N - 1} \times] 0, + \infty [$ . As a consequence, we derive some comparison p…

math.FA2016★ 25 cited

Improved L $^{p}$ -Poincaré inequalities on the hyperbolic space

Elvise Berchio, Lorenzo D'Ambrosio, Debdip Ganguly +1

We investigate the possibility of improving the $p$ -Poincaré inequality $∥ \nabla_{H^{N}} u ∥_{p} \geq Λ_{p} ∥ u ∥_{p}$ on the hyperbolic space, where $p > 2$ and $Λ_p:=[(N-1)/p]^{p}…

math.AP2014★ 49 cited

Some Liouville theorems for the fractional Laplacian

Wenxiong Chen, Lorenzo D'Ambrosio, Yan Li

In this paper, we prove the following result. Let $α$ be any real number between $0$ and $2$ . Assume that $u$ is a solution of $$ \left\{\begin{array}{ll} (-Δ)^{α/2} u(x) = 0 , \;\…

math.AP2012★ 1 cited

Uniqueness of σ-regular solutions of quasilinear elliptic problems

Lorenzo D'Ambrosio, Enzo Mitidieri

We study the uniqueness problem of $σ$ -regular solution of the equation, $$-Δ_p u+ \abs u^{q-1}u =h \quad on\quad \RN, $$ where $q > p - 1 > 0.$ and $N > p .$ Other coercive type equations…

math.AP2012

Hardy inequalities on Riemannian manifolds and applications

Lorenzo D'Ambrosio, Serena Dipierro

We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $Δ_{p}u := \Div(\abs{\nabl…

math.AP2012★ 14 cited

A new critical curve for a class of quasilinear elliptic systems

Lorenzo D'Ambrosio

We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given b…