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Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2
We prove that in arbitrary Carnot groups $\mathbb G$ of step 2, with a splitting $\mathbb G=\mathbb W\cdot\mathbb L$ with $\mathbb L$ one-dimensional, the graph of a continuous functionExpand
Fine properties of functions with bounded variation in Carnot-Carath\'eodory spaces
We study properties of functions with bounded variation in Carnot-Ca\-ra\-theo\-do\-ry spaces. We prove their almost everywhere approximate differentiability and we examine their approximateExpand
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
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 which the DeExpand
A rectifiability result for finite-perimeter sets in Carnot groups
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 that is possibly,Expand
Rank-one theorem and subgraphs of BV functions in Carnot groups
We prove a rank-one theorem \`a la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes Heisenberg groups $\mathbb H^n$ for $n\geq 2$.Expand
Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups
In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These graphs are $C^1_H$ regular exactly when the map is uniformly intrinsically differentiable. Our first mainExpand
Lipschitz minimizers for a class of integral functionals under the bounded slope condition
We consider the functional $\int_\Omega g(\nabla u+\textbf X^\ast)d\mathscr L^{2n}$ where $g$ is convex and $\textbf X^\ast(x,y)=2(-y,x)$ and we study the minimizers in $BV(\Omega)$ of the associatedExpand
A compactness result for BV functions in metric spaces
We prove a compactness result for bounded sequences $(u_j)_j$ of functions with bounded variation in metric spaces $(X,d_j)$ where the space $X$ is fixed but the metric may vary with $j$. We alsoExpand