Prof. Dr. Alessio Figalli

Evolution equations and gradient flows

Published/accepted papers

  1. The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains (with M. Bonforte)
    Nonlinear Anal. 239 (2024), no. 113394.
  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.