Calculus of Variations

Published/accepted papers

  1. Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 (with A. Belotto da Silva, A. Parusiński and L. Rifford)
    Invent. Math. 229 (2022), no. 1, 395–448.
  2. An obstacle problem for conical deformations of thin elastic sheets (with C. Mooney)
    Arch. Ration. Mech. Anal., 228 (2018), no. 2, 401-429.
  3. On supporting hyperplanes to convex bodies (with Y.-H. Kim and R. J. McCann)
    Methods Appl. Anal. 20 (2013), no. 3, 261-271.
  4. On the shape of liquid drops and crystals in the small mass regime (with F. Maggi)
    Arch. Ration. Mech. Anal. 201 (2011), no. 1, 143-207.
  5. Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials (with V. Mandorino)
    Discrete Contin. Dyn. Syst. 31 (2011), no. 4, 1325-1346.
  6. Geodesics in the space of measure-preserving maps and plans (with L. Ambrosio)
    Arch. Ration. Mech. Anal. 194 (2009), no. 2, 421-462.
  7. Generalized solutions for the Euler equations in one and two dimensions (with M. Bernot and F. Santambrogio)
    J. Math. Pures Appl. 91 (2008), no. 2, 137-155.
  8. On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations (with L. Ambrosio)
    Calc. Var. Partial Differential Equations 31 (2008), no. 4, 497-509.

Surveys and lecture notes

  1. Lecture notes on variational models for incompressible Euler equations (with L. Ambrosio)
    Optimal transportation, 58-71, London Math. Soc. Lecture Note Ser. 413, Cambridge Univ. Press, Cambridge, 2014.
  2. Variational models for the incompressible Euler equations (with S. Daneri)
    HCDTE lecture notes. Part II. Nonlinear hyperbolic PDEs, dispersive and transport equations, 51 pp., AIMS Ser. Appl. Math. 7, Am. Inst. Math. Sci. (AIMS), Springfield, MO, 2013.
  3. Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals
    Concentration, functional inequalities and isoperimetry, 77-87, Contemp. Math. 545, Amer. Math. Soc., Providence, RI, 2011.
  4. Optimal transport, Euler equations, Mather and DiPerna-Lions theories.
    Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009.