Papers




On L1stability 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):333378, 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 HamiltonJacobi 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 alphaconvex balance laws, Commun. Pure Appl. Anal., 16(2):629644, 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):101160, 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):11681173, 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 BaitiJenssen system, joint work with Laura V. Spinolo, Networks and Heterogeneous Media, 11(2):263280, 2016 


A note on regularity and failure of regularity for systems of conservation laws via Lagrangian formulation, Bull. Braz. Math. Soc., 47(1):211225, 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):925963, 2015 


A counterexample 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, 8:399406, 2014 


SBV Regularity Results for Solutions to 1D Conservation Laws, Hyperbolic conservation laws and related analysis, Springer Proceedings in Mathematics & Statistics, 49:6985, 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, 43:3152, 2011 


A proof of Sudakov theorem with strictly convex norms, Math. Z., 268:371407, 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 ccyclically 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 Glimmtype 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. 1416, 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. 2329, 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. 1418, 2013—Fluid Mechanic, Hamiltonian Dynamics, and Numerical Aspects of Optimal Transportation, MSRI Berkeley, California, School and Workshop 
Jul. 812, 2013—Vectorvalued Partial Differential Equations and Applications, Cetraro (IT) 
Apr. 1619, 2013—OxfordSJTU 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 FermiPastaUlamtype Model 

