Nicola Garofalo

activity

20152026

collaborators

12 papers

math.AP2026

Heat flow and the fundamental solution of the Baouendi-Grushin operator

Nicola Garofalo

For the Baouendi-Grushin operator $L_{γ} = Δ_{x} + ∣ x ∣^{2 γ} Δ_{y}$ in $R^{m + k}$ , with $γ > 0$ , we prove that the time integral of the heat kernel with pole at the origin equals $C_…

math.AP2026

The Schrödinger Ornstein--Uhlenbeck flow: dispersion, restriction and nonlinear dynamics

Nicola Garofalo

We study the Schrödinger evolution generated by the isotropic Ornstein--Uhlenbeck operator \[ \mathscr L=Δ-\langle x,\nabla\rangle \] in $L^{2} (R^{d}, d γ)$ , where $d γ$ is the in…

math.AP2026

Fractional operators and Sobolev spaces on homogeneous groups

Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev

We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.

math.AP2025

Fractal Mehler kernels and nonlinear geometric flows

Nicola Garofalo

In this paper we introduce a two-parameter family of Mehler kernels and connect them to a class of Baouendi-Grushin flows in fractal dimension. We also highlight a link with a geom…

math.AP2025

Dispersive equations with invariant measures

Nicola Garofalo

In mathematical physics it is of interest to study Schrödinger equations with friction and possessing an invariant measure. The focus of this paper is the Cauchy problem for the Sc…

math.AP2025

Overdetermined fractional Serrin problem

Nicola Garofalo, Dimiter Vassilev

We solve a version of the Serrin overdetermined problem for the Weinstein operator involving a Bessel operator.

math.AP2024

Uncertainty principles for the imaginary Ornstein-Uhlenbeck operator

Nicola Garofalo

We prove two forms of uncertainty principle for the Schrödinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) resu…

math.AP2024

On an evolution equation in sub-Finsler geometry

Nicola Garofalo

We study the gradient flow of an energy with mixed homogeneity which is at the interface of Finsler and sub-Riemannian geometry

math.AP2024

Positive solutions of a critical equation in sub-Finsler geometry

Nicola Garofalo, Paolo Salani

We compute a two-parameter family of explicit positive solutions of a critical Yamabe type equation for a nonlinear operator that sits at the intersection of Finsler and sub-Rieman…

math.AP2024

A fundamental solution for a subelliptic operator in Finsler geometry

Federica Dragoni, Nicola Garofalo, Gianmarco Giovannardi +1

We introduce a class of nonlinear partial differential equations in a product space which are at the interface of Finsler and sub-Riemannian geometry. To such equations we associat…

math.AP2023

Overdetermined problems in groups of Heisenberg type: conjectures and partial results

Nicola Garofalo, Dimiter Vassilev

In this paper we formulate some conjectures in sub-Riemannian geometry concerning a characterisation of the Koranyi-Kaplan ball in a group of Heisenberg type through the existence…

math.AP2015

Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift

Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop +1

We establish the $C^{1 + γ}$ -Hölder regularity of the regular free boundary in the stationary obstacle problem defined by the fractional Laplace operator with drift in the subcritica…