email: xavier.fernandez-real at epfl dot ch
Institute of Mathematics, MA C2 567
Station 8, CH-1015 Lausanne, Switzerland
I am an Ambizione Fellow at EPFL.
My research focuses in PDEs and Calculus of Variations.
In particular, I have worked in elliptic and parabolic PDE, integro-differential equations, obstacle-type problems, transport equations, etc.
Generic properties in free boundary problems,
Xavier Fernández-Real, Hui Yu
Submitted, available at arXiv.
Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels,
Xavier Fernández-Real, Xavier Ros-Oton
Submitted, available at arXiv.
Smooth approximations for fully nonlinear nonlocal elliptic equations,
Xavier Fernández-Real
Trans. Amer. Math. Soc. 377 (2024), 495-515.
Graphical solutions to one-phase free boundary problems,
Max Engelstein, Xavier Fernández-Real, Hui Yu
J. Reine Angew. Math. 804 (2023), 155-195.
Infinite-width limit of deep linear neural networks,
Lénaïc Chizat, Maria Colombo, Xavier Fernández-Real, Alessio Figalli
Comm. Pure Appl. Math., to appear.
Generic regularity of free boundaries for the thin obstacle problem,
Xavier Fernández-Real, Clara Torres-Latorre
Adv. Math. 433 (2023), 109323.
Optimal regularity for the fully nonlinear thin obstacle problem,
Maria Colombo, Xavier Fernández-Real, Xavier Ros-Oton
J. Eur. Math. Soc., to appear.
Improved regularity of second derivatives for subharmonic functions,
Xavier Fernández-Real, Riccardo Tione
Proc. Amer. Math. Soc. 151 (2023), 5283-5297.
Stable cones in the thin one-phase problem,
Xavier Fernández-Real, Xavier Ros-Oton
Amer. J. Math., to appear.
Free boundary regularity for almost every solution to the Signorini problem,
Xavier Fernández-Real, Xavier Ros-Oton
Arch. Ration. Mech. Anal. 240 (2021), 419-466.
On the obstacle problem for the 1D wave equation,
Xavier Fernández-Real, Alessio Figalli
Mathematics in Engineering 2 (2020), 584-597.
Xavier Fernández-Real, Yash Jhaveri
Anal. PDE, 14 (2021), 1599-1669.
On global solutions to semilinear elliptic equations related to the one-phase free boundary problem,
Xavier Fernández-Real, Xavier Ros-Oton
Discrete Contin. Dyn. Syst. A 39 (2019), 6945-6959.
Regularity of minimal surfaces with lower dimensional obstacles,
Xavier Fernández-Real, Joaquim Serra
J. Reine Angew. Math. 767 (2020), 37-75.
The Lagrangian structure of the Vlasov-Poisson system in domains with specular reflection,
Xavier Fernández-Real
Commun. Math. Phys. 364 (2018), 1327-1406.
The obstacle problem for the fractional Laplacian with critical drift,
Xavier Fernández-Real, Xavier Ros-Oton
Math. Ann. 371(3) (2018), 1683-1735.
C1,α estimates for the fully nonlinear Signorini problem,
Xavier Fernández-Real
Calc. Var. Partial Differential Equations (2016), 55:94.
Regularity theory for general stable operators: parabolic equations,
Xavier Fernández-Real, Xavier Ros-Oton
J. Funct. Anal. 270 (2017), no. 10, 4165-4221.
Boundary regularity for the fractional heat equation,
Xavier Fernández-Real, Xavier Ros-Oton
Rev. Acad. Cienc. Ser. A Math. 110 (2016), 49-64.
The continuous formulation of shallow neural networks as Wasserstein-type gradient flows,
Xavier Fernández-Real, Alessio Figalli
In: Analysis at large, Springer 2022.
The thin obstacle problem: a survey,
Xavier Fernández-Real
Publ. Mat. 66 (2022), 3-55.
Integro-Differential Elliptic Equations,
Xavier Fernández-Real, Xavier Ros-Oton
Progress in Mathematics, vol. 350, Birkhäuser, 2024.
Last updated: 2023/08/28. There are many typos. We would appreciate it if you could let us know in case you find any.Regularity Theory for Elliptic PDE,
Xavier Fernández-Real, Xavier Ros-Oton
Zurich Lectures in Advanced Mathematics, EMS Press, 2022.
Last updated: 2023/10/10