Prof. Dr. Alessio Figalli

Non-local energies and elliptic operators

Published/accepted papers

  1. Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (with M. Bonforte and J. L. Vázquez)
    Calc. Var. Partial Differential Equations, 57 (2018), no. 2, Art. 57, 34 pp.
  2. Geometry of minimizers for the interaction energy with mildly repulsive potentials (with J. A. Carrillo and F. S. Patacchini)
    Ann. Inst. H. Poincaré Anal. Non Linéaire, 34 (2017), no. 5, 1299-1308.
  3. Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature (with G. Ciraolo, F. Maggi, and M. Novaga)
    J. Reine Angew. Math. 741 (2018), 275-294.
  4. Regularity and Bernstein-type results for nonlocal minimal surfaces (with E. Valdinoci)
    J. Reine Angew. Math. 729 (2017), 263-273.
  5. Isoperimetry and stability properties of balls with respect to nonlocal energies (with N. Fusco, F. Maggi, V. Millot, and M. Morini)
    Comm. Math. Phys. 336 (2015), no. 1, 441-507.
  6. Strongly nonlocal dislocation dynamics in crystals (with S. Dipierro and E. Valdinoci)
    Comm. Partial Differential Equations 39 (2014), no. 12, 2351-2387.
  7. Bootstrap regularity for integro-differential operators, and its application to nonlocal minimal surfaces (with B. Barrios Barrera and E. Valdinoci)
    Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 13 (2014), no. 3, 609-639.
  8. Asymptotics of the s-perimeter as s --> 0 (with S. Dipierro, G. Palatucci, and E. Valdinoci)
    Discrete Contin. Dyn. Syst. 33 (2013), no. 7, 2777-2790.
  9. Non-Local Gradient Dependent Operators (with C. Bjorland and L. Caffarelli)
    Adv. Math. 230 (2012), no. 4-6, 1859-1894.
  10. Confinement in nonlocal interaction equations (with J. A. Carrillo, M. Di Francesco, T. Laurent, and D. Slepcev)
    Nonlinear Anal. 75 (2012), no. 2, 550-558.
  11. Non-Local Tug-of-War and the Infinity Fractional Laplacian (with C. Bjorland and L. Caffarelli)
    Comm. Pure Appl. Math. 65 (2012), no. 3, 337-380.

Surveys and lecture notes

  1. Regularity theory for local and nonlocal minimal surfaces: an overview (with M. Cozzi)
    Nonlocal and nonlinear diffusions and interactions: new methods and directions, 117-158,
    Lecture Notes in Math., 2186, Fond. CIME/CIME Found. Subser., Springer, Cham, 2017.