9 citations · 19 across the 14 of their papers we have counts for
23 papers
Regularity for the prescribed vertical mean curvature system in the plane
Jonas Hirsch, Connor Mooney, Riccardo Tione
We prove everywhere regularity for Lipschitz solutions to the prescribed vertical mean curvature system in the plane, where the codimension is arbitrary and the mean curvature is i…
Sharp Higher Integrability Theory, Part I: The -norm of the Beurling--Ahlfors transform
Andrea Agazzi, Kari Astala, Giuseppe Bruno +18
We confirm a conjecture posed by T. Iwaniec in 1982: the norm of the Beurling--Ahlfors transform is if , and if .
Stationary points of conformally invariant polyconvex energies
André Guerra, Riccardo Tione
We consider polyconvex integrands that are conformally invariant and frame indifferent. In two dimensions, we prove that the corresponding stationary points are smooth outside a di…
Rigidity of shear flows of the Euler equations in the plane
Riccardo Tione
In this paper we show that steady states of the pressureless Euler equation which belong to are shear flows. This is achieved by combinin…
On the Lawson-Osserman conjecture
Jonas Hirsch, Connor Mooney, Riccardo Tione
We prove that if is a Lipschitz critical point of the area functional with respect to outer variations, then is smooth.…
The double and triple bubble problem for stationary varifolds: the convex case
Antonio De Rosa, Riccardo Tione
We characterize the critical points of the double bubble problem in and the triple bubble problem in , in the case the bubbles are convex.
Fine properties of symmetric and positive matrix fields with bounded divergence
Luigi De Rosa, Riccardo Tione
This paper is concerned with various fine properties of the functional \[ \mathbb{D}(A) = \int_{\mathbb{T}^n}{\text{det}}^\frac{1}{n-1}(A(x))\,dx \] introduced in [33]. This functi…
configurations and hyperbolic systems
Carl Johan Peter Johansson, Riccardo Tione
In this paper we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in Sect…
Critical points of degenerate polyconvex energies
Riccardo Tione
We study critical and stationary, i.e. critical with respect to both inner and outer variations, points of polyconvex functionals of the form , for $X \in \mathb…
Non-classical solutions of the -Laplace equation
Maria Colombo, Riccardo Tione
In this paper we answer Iwaniec and Sbordone's conjecture \cite{IB94} concerning very weak solutions to the -Laplace equation. Namely, on one hand we show that distributional so…
Improved regularity of second derivatives for subharmonic functions
Xavier Fernández-Real, Riccardo Tione
In this note, we prove that if a subharmonic function has pure second derivatives that are signed measures, then their negative part $(\partial_{ii} u)_…
The four-state problem and convex integration for linear differential operators
Massimo Sorella, Riccardo Tione
We show that the four-state problem for general linear differential operators is flexible. The only flexibility result available in this context is the one for the five-state probl…
Regularity for graphs with bounded anisotropic mean curvature
Antonio De Rosa, Riccardo Tione
We prove that -dimensional Lipschitz graphs with anisotropic mean curvature bounded in , , are regular almost everywhere in every dimension and codimension. This provi…
On the commutativity of flows of rough vector fields
Maria Colombo, Riccardo Tione
In the class of Sobolev vector fields in of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the…
On the constancy theorem for anisotropic energies through differential inclusions
Jonas Hirsch, Riccardo Tione
In this paper we study stationary graphs for functionals of geometric nature defined on currents or varifolds. The point of view we adopt is the one of differential inclusions, int…
Minimal graphs and differential inclusions
Riccardo Tione
In this paper, we study the differential inclusion associated to the minimal surface system for two-dimensional graphs in . We prove regularity of sol…
Geometric measure theory and differential inclusions
Camillo De Lellis, Guido De Philippis, Bernd Kirchheim +1
In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifold…
Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations
Luigi De Rosa, Riccardo Tione
This paper is devoted to show a couple of typicality results for weak solutions of the Euler equations, in the case . It is known that convex integration schemes…
On the upper semicontinuity of a quasiconcave functional
Luigi De Rosa, Denis Serre, Riccardo Tione
In the recent paper \cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \mathbb{D}(A)=\int_{\mathbb{T}^n} det(A(x))^{\frac{1}…
The oriented mailing problem and its convex relaxation
Marcello Carioni, Andrea Marchese, Annalisa Massaccesi +2
In this note we introduce a new model for the mailing problem in branched transportation in order to allow the cost functional to take into account the orientation of the moving pa…
On a question of D. Serre
Luigi De Rosa, Riccardo Tione
In this paper we give a negative answer to the question posed in [15, Open Question 2.1] about possible gains of integrability of determinants of divergence-free, non-negative defi…
A multi-material transport problem with arbitrary marginals
Andrea Marchese, Annalisa Massaccesi, Salvatore Stuvard +1
In this paper we study general transportation problems in , in which different goods are moved simultaneously. The initial and final positions of the goods are pr…
A multi-material transport problem and its convex relaxation via rectifiable -currents
Andrea Marchese, Annalisa Massaccesi, Riccardo Tione
In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities…