5 papers · 1 filter
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…
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…
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…
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…
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…