4 papers
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 spaces for Fokker-Planck and transport-diffusion equations under two new assumptions on their velocity field $b=b(x,t…
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…
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…
The prescribed mean curvature equation for -graphs in the sub-Finsler Heisenberg group
Gianmarco Giovannardi, Andrea Pinamonti, Julián Pozuelo +1
We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body , for -graphs on a bounded domain in the He…