# Evolution equations and gradient flows

### Published/accepted papers

- Infinite-width limit of deep linear neural networks (with L. Chizat, M. Colombo, X. Fernández-Real)
- Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (with M. Bonforte)

*Comm. Pure Appl. Math.* 74 (2021), no. 4, 744–789.
- 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.
- 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.
- 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.
- 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.
- 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.
- Total Variation Flow and Signed Fast Diffusion in one dimension (with M. Bonforte)

*J. Differential Equations* 252 (2012), no. 8, 4455-4480.
- 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 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.
- 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

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

*Preprint* 2022.