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

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8 papers · 1 filter

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.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…

math.AP2012

Entire solutions of quasilinear elliptic systems on Carnot Groups

Lorenzo D'Ambrosio, Enzo Mitidieri

We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems. The results…