Alessio Figalli - Selected Publications#

On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)
Invent. Math., 215 (2019), no. 1, 311-366.

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.

Universality in several-matrix models via approximate transport maps (with A. Guionnet)
Acta Math. 217 (2016), no. 1, 81-176.

Partial regularity for optimal transport maps (with G. De Philippis)
Publ. Math. Inst. Hautes Études Sci. 121 (2015), 81-112.

Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)
Invent. Math. 200 (2015), no. 1, 201-261.

Higher integrability for minimizers of the Mumford-Shah functional (with G. De Philippis)
Arch. Ration. Mech. Anal. 213 (2014), no. 2, 491-502.

Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass
Keller-Segel equation (with E. Carlen)
Duke Math. J. 162 (2013), no. 3, 579-625.

W2,1 regularity for solutions of the Monge-Ampère equation (with G. De Philippis)
Invent. Math. 192 (2013), no. 1, 55-69.

Global in time measure-valued solutions and finite-time aggregation for nonlocal interaction equations
(with J. A. Carrillo, M. Di Francesco, T. Laurent, and D. Slepcev)
Duke Math. J. 156 (2011), no. 2, 229-271.

A mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
Invent. Math. 182 (2010), no. 1, 167-211.