41 citations · 45 across the 6 of their papers we have counts for
7 papers
-free measures and the Rank-one Theorem in Carnot Groups
Guido De Philippis, Alberto Gervani, Annalisa Massaccesi +1
We establish a structure theorem for measures satisfying left-invariant PDE constraints in Carnot groups. Our generalization, that takes inspiration from the paper arxiv:1601.06543…
Besicovitch's 1/2 problem and linear programming
Camillo De Lellis, Federico Glaudo, Annalisa Massaccesi +1
We consider the following classical conjecture of Besicovitch: a -dimensional Borel set in the plane with finite Hausdorff -dimensional measure which has lowe…
On the boundary behavior of mass-minimizing integral currents
Camillo De Lellis, Guido De Philippis, Jonas Hirsch +1
Let be a smooth Riemannian manifold, a smooth closed oriented submanifold of codimension higher than and an integral area-minimizing current in which b…
Boundary regularity of mass-minimizing integral currents and a question of Almgren
Camillo De Lellis, Guido De Philippis, Jonas Hirsch +1
This short note is the announcement of a forthcoming work in which we prove a first general boundary regularity result for area-minimizing currents in higher codimension, without a…
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^…
The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system
Maria Colombo, Camillo De Lellis, Annalisa Massaccesi
We introduce a notion of suitable weak solution of the hyperdissipative Navier-Stokes equations and we achieve a corresponding extension of the regularity theory of Caffarelli-Kohn…
An elementary proof of the rank-one theorem for BV functions
Annalisa Massaccesi, Davide Vittone
We provide a simple proof of a result, due to G. Alberti, concerning a rank-one property for the singular part of the derivative of vector-valued functions of bounded variation.