# Transport equations

### Published/accepted papers

- On the prescribed negative Gauss curvature problem for graphs (with Ch. Kehle)
*Discrete Contin. Dyn. Syst.*, to appear - On the Lagrangian structure of transport equations: the Vlasov-Poisson system(with L. Ambrosio and M. Colombo)
*Duke Math. J.*166 (2017), no. 18, 3505-3568. - Existence and uniqueness of maximal regular flows for non-smooth vector fields (with L. Ambrosio and M. Colombo)

*Arch. Ration. Mech. Anal.*218 (2015), no. 2, 1043-1081. - WKB analysis of Bohmian dynamics (with C. Klein, P. Markowich, and C. Sparber)

*Comm. Pure Appl. Math.*67 (2014), no. 4, 581-620. - A global existence result for the semigeostrophic equations in three dimensional convex domains (with L. Ambrosio, M. Colombo, and G. De Philippis)

*Discrete Contin. Dyn. Syst.*34 (2014), no. 4, 1251-1268. - Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (with L. Ambrosio, M. Colombo, and G. De Philippis)

*Comm. Partial Differential Equations*37 (2012), no. 12, 2209-2227. - Semiclassical limit for mixed states with singular and rough potentials (with M. Ligabò and T. Paul)

*Indiana Univ. Math. J.*61 (2012), no. 1, 193-222. Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (with L. Ambrosio, G. Friesecke, J. Giannoulis, and T. Paul)

*Comm. Pure Appl. Math.*64 (2011), no. 9, 1199-1242.- Almost everywhere well-posedness of continuity equations with measure initial data (with L. Ambrosio)

*C. R. Math. Acad. Sci. Paris*348 (2010), no. 5-6, 249-252. - Some new well-posedness results for continuity and transport equations, and applications to the chromatography system (with L. Ambrosio, G. Crippa, and L. V. Spinolo)

*SIAM J. Math. Anal.*41 (2009), no. 5, 1890-1920. - On flows associated to Sobolev vector fields in Wiener spaces: an approach à la DiPerna-Lions (with L. Ambrosio)

*J. Funct. Anal.*256 (2009), no.1, 179-214.

### Surveys and lecture notes

- Existence and uniqueness results for the continuity equation and applications to the chromatography system (with L. Ambrosio, G. Crippa and L. V. Spinolo)

Nonlinear conservation laws and applications, 195-204,*IMA Vol. Math. Appl.*153, Springer, New York, 2011. - Almost everywhere well-posedness of continuity equations with measure initial data (with L. Ambrosio)

*C. R. Math. Acad. Sci. Paris*348 (2010), no. 5-6, 249-252. - Optimal transport, Euler equations, Mather and DiPerna-Lions theories.

Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009