Gianmarco Giovannardi

activity

20192026

most citedVariational formulas for submanifolds of fixed degree

8 citations · 16 across the 15 of their papers we have counts for

collaborators

15 papers

math.AP2026

Transport-diffusion equations with irregular data and applications to stability estimates for second-order Hamilton-Jacobi PDEs

Gianmarco Giovannardi, Alessandro Goffi

This paper studies quantitative uniqueness properties in $L^{p}$ spaces for Fokker-Planck and transport-diffusion equations under two new assumptions on their velocity field $b=b(x,t…

math.DG2024★ 1 cited

Curvature estimates for minimal hypersurfaces in the Heisenberg group

Gianmarco Giovannardi, Andrea Pinamonti, Simone Verzellesi

This paper examines minimal hypersurfaces in sub-Riemannian Heisenberg groups. We extend the celebrated Simons formula and Kato inequality to the sub-Riemannian setting, and we app…

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

Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups

Fares Essebei, Gianmarco Giovannardi, Simone Verzellesi

In this paper we study Monge solutions to stationary Hamilton-Jacobi equations associated to discontinuous Hamiltonians in the framework of Carnot groups. After showing the equival…

math.AP2023

An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems

Gianmarco Giovannardi, Dimitri Mugnai, Eugenio Vecchi

We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appe…

math.AP2023

The asymptotic $p$ -Poisson equation as $p \to \infty$ in Carnot-Carathéodory spaces

Luca Capogna, Gianmarco Giovannardi, Andrea Pinamonti +1

In this paper we study the asymptotic behavior of solutions to the subelliptic $p$ -Poisson equation as $p \to + \infty$ in Carnot Carathéodory spaces. In particular, introducing a su…

math.AP2022

The prescribed mean curvature equation for $t$ -graphs in the sub-Finsler Heisenberg group $H^{n}$

Gianmarco Giovannardi, Andrea Pinamonti, Julián Pozuelo +1

We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body $K_{0} \subseteq R^{2 n}$ , for $t$ -graphs on a bounded domain $Ω$ in the Hei…

math.DG2022

Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $H^{1}$

Gianmarco Giovannardi, Julián Pozuelo, Manuel Ritoré

In the Heisenberg group $H^{1}$ , equipped with a left-invariant and not necessarily symmetric norm in the horizontal distribution, we provide examples of entire area-minimiz…

math.DG2021

The Bernstein problem for $(X, Y)$ -Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups

Gianmarco Giovannardi, Manuel Ritoré

We prove that in the Heisenberg group $H^{1}$ with a sub-Finsler structure, an $(X, Y)$ -Lipschitz surface which is complete, oriented, connected and stable must be a vertical…

math.AP2021

Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential

Giovanna Citti, Gianmarco Giovannardi, Yannick Sire

We establish the Schauder estimates at the boundary away from the characteristic points for the Dirichlet problem by means of the double layer potential in a Heisenberg-type group…

math.AP2020

Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry

Sylvester Eriksson-Bique, Gianmarco Giovannardi, Riikka Korte +2

We study existence, uniqueness, and regularity properties of the Dirichlet problem related to fractional Dirichlet energy minimizers in a complete doubling metric measure space $(X…

math.DG2020★ 7 cited

Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group $H^{1}$

Gianmarco Giovannardi, Manuel Ritoré

For a strictly convex set $K \subset R^{2}$ of class $C^{2}$ we consider its associated sub-Finsler $K$ -perimeter $∣ \partial E ∣_{K}$ in $H^{1}$ and the prescribed mean cur…

math.DG2019

Higher dimensional holonomy map for ruled submanifolds in graded manifolds

Gianmarco Giovannardi

The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of…

math.DG2019★ 8 cited

Variational formulas for submanifolds of fixed degree

Giovanna Citti, Gianmarco Giovannardi, Manuel Ritoré

We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this…

math.MG2019

Variational formulas for curves of fixed degree

Giovanna Citti, Gianmarco Giovannardi, Manuel Ritoré

We consider a length functional for $C^{1}$ curves of fixed degree in graded manifolds equipped with a Riemannian metric. The first variation of this length functional can be compute…

Transport-diffusion equations with irregular data and applications to stability estimates for second-order Hamilton-Jacobi PDEs

Curvature estimates for minimal hypersurfaces in the Heisenberg group

A fundamental solution for a subelliptic operator in Finsler geometry

Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups

An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems

The asymptotic p-Poisson equation as p→∞ in Carnot-Carathéodory spaces

The prescribed mean curvature equation for t-graphs in the sub-Finsler Heisenberg group Hn

Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group H1

The Bernstein problem for (X,Y)-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups

Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential

Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry

Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group H1

Higher dimensional holonomy map for ruled submanifolds in graded manifolds

Variational formulas for submanifolds of fixed degree

Variational formulas for curves of fixed degree

The asymptotic $p$ -Poisson equation as $p \to \infty$ in Carnot-Carathéodory spaces

The prescribed mean curvature equation for $t$ -graphs in the sub-Finsler Heisenberg group $H^{n}$

Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $H^{1}$

The Bernstein problem for $(X, Y)$ -Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups

Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group $H^{1}$