# Research

## Papers

On L1-stability of BV solutions for a model of granular flow, joint work with Fabio Ancona, Cleopatra Christoforou, Proceeding of the 17th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2018), AIMS Series on Applied Mathematics, 10, 2020
On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function, joint work with Fabio Ancona, Andrea Marson, J. Hyperbolic Differ. Equ., 16(2):333-378, 2019
A Directional Lipschitz Extension Lemma, with Applications to Uniqueness and Lagrangianity for the Continuity Equation, joint work with Gianluca Crippa, Accepted for publication on Communications in Partial Differential Equations, 2019,

https://arxiv.org/abs/1812.06817

Preface: Recent developments related to conservation laws and Hamilton-Jacobi equations, joint work with Annalisa Cesaroni, Hung Vinh Tran, Discrete & Continuous Dynamical Systems - S, 11(5), 2018,

https://doi.org/10.3934/dcdss.201805i

Preface to Analysis and control on networks: Trends and perspectives, joint work with Fabio Ancona, Giuseppe Maria Coclite, Annalisa Cesaroni, Claudio Marchi, Andrea Marson, NHM, 12(3), 2017
Preface to Analysis and control on networks: Trends and perspectives, joint work with Fabio Ancona, Giuseppe Maria Coclite, Annalisa Cesaroni, Claudio Marchi, Andrea Marson, NHM, 12(2), 2017
Regularity estimates for continuous solutions of alpha-convex balance laws, Commun. Pure Appl. Anal., 16(2):629-644, 2017,

doi:10.3934/cpaa.2017031

Schaeffer's regularity theorem for scalar conservation laws does not extend to systems, joint work with Laura V. Spinolo, Indiana Univ. Math. J., 66(1):101-160, 2017
Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation, joint work with G. Crippa, C. R. Math. Acad. Sci. Paris, Ser. I, 354(12):1168-1173, 2016
Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II, joint work with G. Alberti, S. Bianchini, 2016,

Preprint SISSA 32/2016/MATE. *preliminary version of the paper*
http://preprints.sissa.it/xmlui/handle/1963/35197

Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux I, joint work with G. Alberti, S. Bianchini, J. Differential Equations, 261(8):4298–4337, 2016,

Listen here to the AudioSlides

New interaction estimates for the Baiti-Jenssen system, joint work with Laura V. Spinolo, Networks and Heterogeneous Media, 11(2):263-280, 2016
A note on regularity and failure of regularity for systems of conservation laws via Lagrangian formulation, Bull. Braz. Math. Soc., 47(1):211-225, 2016
Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation, joint work with F. Bigolin and F. Serra Cassano, Ann. Inst. H. Poincaré Anal. Non Linéaire, 32(5):925-963, 2015
A counter-example concerning regularity properties for systems of conservation laws, joint work with L. Spinolo, PAMM, 15(1):625–626, 2015,

Nontechnical communication

Reduction on characteristics for continuous solutions of a scalar balance law, joint work with G. Alberti, S. Bianchini, Hyperbolic Problems: Theory, Numerics, Applications, AIMS, 8:399-406, 2014
SBV Regularity Results for Solutions to 1D Conservation Laws, Hyperbolic conservation laws and related analysis, Springer Proceedings in Mathematics & Statistics, 49:69-85, 2014
SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension, joint work with S. Bianchini, Comm. Math. Phys. 313(1):1–33, 2012.
A proof of Monge problem in $\mathbb{R}^n$ by stability, Rend. Istit. Mat. Univ. Trieste, 43:31-52, 2011
A proof of Sudakov theorem with strictly convex norms, Math. Z., 268:371-407, 2011
The disintegration of the Lebesgue measure on the faces of a convex function, joint work with S. Daneri, J. Funct. Anal., 258(11):3604–3661, 2010
On optimality of c-cyclically monotone transference plans, joint work with S. Bianchini, C. R. Math. Acad. Sci. Paris, Ser. I, 348:613–618, 2010
On the extremality, uniqueness and optimality of transference plans, joint work with S. Bianchini, Bull. Inst. Math. Acad. Sin. (N.S.), 4(4):353–455, 2009
An entropy based Glimm-type functional, J. Hyperbolic Differ. Equ., 5(3):643–662, 2008

## Selected Talks

Exponential Stability of BV Solutions in a Model of Granular flow Video: https://www.youtube.com/watch?v=Ph9DX6PeuwY, Oct. 17, 2019, PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws, CIRM Marseille, France
A Directional Lipschitz Extension applied to Transport, Jul. 9, 2019, GMT and PDEs in Basel – A young researchers meeting, University of Basel Basel
Fine properties and regularity in conservation laws , Jun. 14-16, 2017, From students to mathematicians, SISSA & Università di Trieste
A simple uniqueness approach for the transport equation with Sobolev, continuous fields, Jun. 14, 2016, 11th Meeting on Nonlinear Hyperbolic PDEs and Applications, On the occasion of the 60th birthday of Alberto Bressan, SISSA Trieste
Generic piecewise smooth solutions and the case of systems of conservation laws, Jun. 25, 2015, Shock waves and beyond, Institut Henri Poincaré, Paris
Regularity results for conservation laws via Lagrangian formulation, Jul. 28, 2014, HYP2014, Rio de Janeiro (Brasil)

see complete list

## Some Short Schools and Conferences Attended

Nov. 23-29, 2014—Analysis of Compressible Navier Stokes Equations and Related Topics, Oberwolfach Seminar
Oct. 2014—Measure valued vector fields, Ferrara (Italy), by Hermano Frid (IMPA, Brazil)
Oct. 14-18, 2013—Fluid Mechanic, Hamiltonian Dynamics, and Numerical Aspects of Optimal Transportation, MSRI Berkeley, California, School and Workshop
Jul. 8-12, 2013—Vector-valued Partial Differential Equations and Applications, Cetraro (IT)
Apr. 16-19, 2013—Oxford-SJTU workshop, Shaghai (PRC)

see complete list

## Thesis

PhD Thesis: The Disintegration Theorem and Applications to Optimal Mass Transportation
MA Thesis: Sulla dissipazione di entropia per leggi di conservazione
BA Thesis: Numerical Observation on a Fermi-Pasta-Ulam-type Model