8 papers
Transport and flow for horizontal Sobolev contact velocities in Carnot groups
Gianluca Somma, Simone Verzellesi, Davide Vittone
We establish new well-posedness results for transport and flow equations driven by contact vector fields on Carnot groups. The velocity fields are assumed to have horizontal Sobole…
Variation formulas for mean curvature functionals
Simone Verzellesi
We establish first and second variation formulas for general mean curvature functionals under arbitrary variations in arbitrary Riemannian manifolds. We obtain corresponding formul…
Serrin problems with vertical boundary behavior
Julián Pozuelo, Simone Verzellesi
We study Serrin-type overdetermined problems for a class of possibly degenerate elliptic operators under a vertical boundary condition forcing gradient blow-up. We identify the pre…
Unexpected phenomena for mean curvature functionals in the Heisenberg group
Mattia Fogagnolo, Andrea Pinamonti, Simone Verzellesi
The Euclidean paradigm that spheres optimize mean curvature variational problems breaks down in the sub-Riemannian Heisenberg group: neither the Pansu sphere nor the Korányi sphere…
Renormalization of contact vector fields with horizontal Sobolev regularity in Heisenberg groups
Luigi Ambrosio, Gianluca Somma, Simone Verzellesi +1
In this paper we obtain the well-posedness of the transport and continuity equations in the Heisenberg groups for a class of contact vector fields , under…
Variational properties of the total inverse mean curvature in the plane under boundary constraints
Julián Pozuelo, Simone Verzellesi, Giacomo Vianello
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with pr…
A survey on anisotropic integral representation results
Simone Verzellesi
In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.
Hypergenerated Carnot groups
Enrico Le Donne, Luca Nalon, Nicola Paddeu +1
In this paper we provide an algebraic characterization of those stratified groups in which boundaries with locally constant normal are locally flat. We show that these groups, whic…