Francesco Serra Cassano
University of Trento
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Featured researches published by Francesco Serra Cassano.
Journal of Geometric Analysis | 2003
Bruno Franchi; Raul Serapioni; Francesco Serra Cassano
In this article we study codimension 1 rectifiable sets in Carnot groups and we extend classical De Giorgi ’s rectifiability and divergence theorems to the setting of step 2 groups. Related problems in higher step Carnot groups are discussed, pointing on new phenomena related to the blow up procedure.
Journal of Geometric Analysis | 2006
Luigi Ambrosio; Francesco Serra Cassano; Davide Vittone
We study the ℍ-regular surfaces, a class of intrinsic regular hypersurfaces in the setting of the Heisenberg group ℍ n = ℂ n × ℝ = ℝ2n+1 endowed with a leftinvariant metric d∞ equivalent to its Carnot-Carathéodory (CC) metric. Here hypersurface simply means topological codimension 1 surface and by the words “intrinsic” and “regular” we mean, respectively notions involving the group structure of ℍ n and its differential structure as CC manifold. In particular, we characterize these surfaces as intrinsic regular graphs inside ℍ n by studying the intrinsic regularity of the parameterizations and giving an areatype formula for their intrinsic surface measure.
Advances in Calculus of Variations | 2010
Francesco Bigolin; Francesco Serra Cassano
Abstract We continue to study ℍ-regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group endowed with a left-invariant metric d ∞ equivalent to its Carnot–Carathéodory metric. Here we investigate their relationships with suitable weak solutions of non-linear first-order PDEs. As a consequence this implies some of their geometric properties: a uniqueness result for ℍ-regular graphs of prescribed horizontal normal as well as their (Euclidean) regularity as long as there is regularity on the horizontal normal.
Potential Analysis | 1998
Bruno Franchi; Raul Serapioni; Francesco Serra Cassano
We give examples of discontinuous solutions and of unbounded solutions of linear isotropic degenerate elliptic equations. Discontinuous solutions exist even when both the maximum eigenvalue and the inverse of the minimum eigenvalue of the matrix of the coefficients are in the intersection of all the Lp spaces.
Advances in Calculus of Variations | 2014
Francesco Serra Cassano; Davide Vittone
Abstract In the setting of the sub-Riemannian Heisenberg group ℍn, we introduce and study the classes of t- and intrinsic graphs of bounded variation. For both notions we prove the existence of non-parametric area-minimizing surfaces, i.e., of graphs with the least possible area among those with the same boundary. For minimal graphs we also prove a local boundedness result which is sharp at least in the case of t-graphs in ℍ1.
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze | 2015
Andrea Pinamonti; Francesco Serra Cassano; Giulia Treu; Davide Vittone
We consider the area functional for t-graphs in the sub-Riemannian Heisenberg group and study minimizers of the associated Dirichlet problem. We prove that, under a bounded slope condition on the boundary datum, there exists a unique minimizer and that this minimizer is Lipschitz continuous. We also provide an example showing that, in the first Heisenberg group, Lipschitz regularity is sharp even under the bounded slope condition.
Mathematische Annalen | 2001
Bruno Franchi; Raul Serapioni; Francesco Serra Cassano
Calculus of Variations and Partial Differential Equations | 2001
Roberto Monti; Francesco Serra Cassano
Communications in Analysis and Geometry | 2003
Francesco Serra Cassano; Bruno Franchi; Raul Serapioni
Advances in Mathematics | 2007
Bruno Franchi; Raul Serapioni; Francesco Serra Cassano