11 citations · 23 across the 12 of their papers we have counts for
13 papers
A BMO-type representation formula for the total variation of SBV functions in Heisenberg groups
Marco Di Marco, Sebastiano Don, Davide Vittone
We prove a formula for the total variation of SBV functions in sub-Riemannian Heisenberg groups arising as the limit of certain BMO-type functionals.
SBV functions in Carnot-Carathéodory spaces
Marco Di Marco, Sebastiano Don, Davide Vittone
We introduce the space SBV of special functions with bounded -variation in Carnot-Carathéodory spaces and study its main properties. Our main outcome is an approximation res…
Surface measure on, and the local geometry of, sub-Riemannian manifolds
Sebastiano Don, Valentino Magnani
We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for…
Weighted Gagliardo-Nirenberg inequalities via Optimal Transport Theory and Applications
Zoltán M. Balogh, Sebastiano Don, Alexandru Kristály
We prove Gagliardo-Nirenberg inequalities with three weights -- verifying a joint concavity condition -- on open convex cones of . If the weights are equal to each oth…
Sharp weighted log-Sobolev inequalities: characterization of equality cases and applications
Zoltán M. Balogh, Sebastiano Don, Alexandru Kristály
By using optimal mass transport theory, we provide a direct proof to the sharp -log-Sobolev inequality involving a log-concave homogeneous weight on an open convex…
Lipschitz minimizers for a class of integral functionals under the bounded slope condition
Sebastiano Don, Luca Lussardi, Andrea Pinamonti +1
We consider the functional where is convex and and we study the minimizers in of the as…
Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2
Gioacchino Antonelli, Daniela Di Donato, Sebastiano Don
We prove that in arbitrary Carnot groups of step 2, with a splitting with one-dimensional, the graph of a continuous fun…
Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups
Gioacchino Antonelli, Daniela Di Donato, Sebastiano Don +1
In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These graphs are regular exactly when the map is uniformly intrinsically differentiable…
Local minimizers and Gamma-convergence for nonlocal perimeters in Carnot Groups
Alessandro Carbotti, Sebastiano Don, Diego Pallara +1
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in…
A rectifiability result for finite-perimeter sets in Carnot groups
Sebastiano Don, Enrico Le Donne, Terhi Moisala +1
In the setting of Carnot groups, we are concerned with the rectifiability problem for subsets that have finite sub-Riemannian perimeter. We introduce a new notion of rectifiability…
Fine properties of functions with bounded variation in Carnot-Carathéodory spaces
Sebastiano Don, Davide Vittone
We study properties of functions with bounded variation in Carnot-Ca\-ra\-théo\-do\-ry spaces. We prove their almost everywhere approximate differentiability and we examine their a…
A compactness result for BV functions in metric spaces
Sebastiano Don, Davide Vittone
We prove a compactness result for bounded sequences of functions with bounded variation in metric spaces where the space is fixed but the metric may vary wi…
Rank-one theorem and subgraphs of BV functions in Carnot groups
Sebastiano Don, Annalisa Massaccesi, Davide Vittone
We prove a rank-one theorem à la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes Heisenberg groups $\mathbb H^…