# Evolution equations and gradient flows

### Published/accepted papers

1. Infinite-width limit of deep linear neural networks (with L. Chizat, M. Colombo, X. Fernández-Real)
2. Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (with M. Bonforte)
Comm. Pure Appl. Math. 74 (2021), no. 4, 744–789.
3. A rigorous derivation from the kinetic cucker-smale model to the pressureless euler system with nonlocal alignment (with M.-J. Kang)
Anal. PDE 12 (2019), no. 3, 843-866.
4. Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (with M. Bonforte and J. L. Vázquez)
Anal. PDE 11 (2018), no. 4, 945-982.
5. Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow (with M.-J. Kang and J. Morales)
Arch. Ration. Mech. Anal. 227 (2018), no. 3, 869-896.
6. Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains (with M. Bonforte and X. Ros-Oton)
Comm. Pure Appl. Math. 70 (2017), no. 8, 1472-1508.
7. 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.
8. Total Variation Flow and Signed Fast Diffusion in one dimension (with M. Bonforte)
J. Differential Equations 252 (2012), no. 8, 4455-4480.
9. 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.
10. A variational method for a class of parabolic PDEs (with W. Gangbo and T. Yolcu)
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 10 (2011), no. 1, 207-252.
11. A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (with N. Gigli)
J. Math. Pures Appl. 94 (2010), no. 2, 107-130.

### Surveys and lecture notes

1. The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains (with M. Bonforte)
Preprint 2022.