1 citations · 1 across the 5 of their papers we have counts for
6 papers
A singular minimizer of a smooth strongly polyconvex functional in two dimensions
André Guerra, Riccardo Tione
We construct a Lipschitz, non- map which is the unique global minimizer of a smooth, strongly polyconvex functional. Such an example is…
Hyperbolic regularization effects for degenerate elliptic equations
Xavier Lamy, Riccardo Tione
This paper investigates the regularity of Lipschitz solutions to the general two-dimensional equation with highly degenerate ellipticity. Just assuming st…
Constancy of the index for gradient mappings
André Guerra, Riccardo Tione
We show that if the Hessian of a function has uniformly positive determinant almost everywhere then its index is locally constant, as conjectured by Šverák in 1992. We de…
Regularity and compactness for critical points of degenerate polyconvex energies
André Guerra, Riccardo Tione
We study Lipschitz critical points of the energy in two dimensions, where is a strictly convex function. We prove that the Jacobian of any Lipschitz…
Unique continuation for differential inclusions
Guido De Philippis, André Guerra, Riccardo Tione
We consider the following question arising in the theory of differential inclusions: given an elliptic set and a Sobolev map whose gradient lies in the quasiconformal envel…
On singular strictly convex solutions to the Monge-Ampère equation
Guido De Philippis, Riccardo Tione
We show the existence of a strictly convex function with associated Monge-Ampère measure represented by a function with a.e. whose Hessian h…