Below you can find a list of my publications and preprints:
(With X. Fernádez-Real) Global solutions to the thin obstacle problem with superqudratic growth, preprint.
(With O. Savin) Concentration of cones in the Alt-Phillips problem, preprint.
(With O. Savin) Stable and minimizing cones in the Alt-Phillips problem, preprint.
(With X. Fernández-Real) Generic properties in free boundary problems, preprint.
(With S. Eberle) Solutions to the nonlinear obstacle problem with compact contact sets, Journal of Functional Analysis 287 (2024), 110589.
(With S. Eberle) Compact contact sets of sub-quadratic solutions to the thin obstacle problem, Advances in Mathematics 444 (2024), 109635.
(With M. Engelstein and X. Fernández-Real) Graphical solutions to one-phase free boundary problems, Journal für die reine und angewandt Mathematik (Crelles Journal) (2023), 155-195.
(With O. Savin) Free boundary regularity in the multiple membrane problem in the plane, Journal für die reine und angewandt Mathematik (Crelles Journal) (2023), 109-154.
(With O. Savin) Half-space solutions with 7/2 frequency in the thin obstacle problem, Archive for Rational Mechanics and Analysis 246 (2022), 397-474.
(With O. Savin) Contact points with integer frequencies in the thin obstacle problem, Communications on Pure and Applied Mathematics 76 (2023), 4048-4074.
(With O. Savin) On the fine regularity of the singular set in the nonlinear obstacle problem, Nonlinear Analysis 218, (2022).
(With Y. Wu) On the fully nonlinear Alt-Phillips equation, International Mathematics Research Notices (2022), 8540-8570.
(With O. Savin) Free boundary regularity in the triple membrane problem, Ars Inveniendi Analytica (2021), Paper No. 3.
(With O. Savin) Regularity of the singular set in the fully nonlinear obstacle problem, Journal of the European Mathematical Society 25 (2023), 571-610.
(With O. Savin) On the multiple membranes problem, Journal of Functional Analysis 277 (2019), 1581-1602.
An optimization problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation, Calculus of Variations and PDEs 55 (2016), 1-15.
(With O. Savin) Global W^{2,1+epsilon) estimates for Monge-Ampére equation with natural boundary condition, Journal de Mathématiques Pures et Appliquées 137 (2020), 275-289.
(With O. Savin) Regularity of optimal transport between planar convex domains, Duke Mathematical Journal 169 (2020), 1305-1327.
(With L. Caffarelli) A curvature flow in the plane with a nonlocal term, Calculus of Variations and PDEs 57 (2018).
Motion of sets by curvature and derivative of capacity potential, Journal of Differential Equations 267 (2019), 15-60.
(With V. Millot and Y. Sire) Minimizing fractional harmonic maps on the real line in the super critical regime, Discrete and Continuous Dynamical Systems-A 38 (2018), 6195-6214.
Unique continuation for fractional orders of elliptic equations, Annals of PDE 3 (2017), artical no. 16.
Small perturbation solutions for nonlocal elliptic equations, Communications in Partial Differential Equations 42 (2017), 142-158.
A Dirichlet problem for nonlocal degenerate elliptic operators with interior nonlinearity, Journal of Mathematical Analysis and Applications 448 (2017), 326-346.
W^{sigma, epsilon}-estimates for nonlocal elliptic equations, Annales de l'Institut H. Poincaré-C 34 (2017), 1141-1153.
Smooth solutions to a class of nonlocal fully nonlinear elliptic equations, Indiana University Mathematics Journal 66 (2015), 1895-1919.
(With S. Aaron, Z. Conn, R. Strichartz) Hodge-de Rham theory on fractal graphs and fractals, Communications on Pure and Applied Analysis 13 (2014), 903-928.
Rigidity of global solutions to the thin obstacle problem, to appear in Oberwolfach Report 2024.
A brief survey on the obstacle problem, to appear in Proceedings of the 8th International Congress of Chinese Mathematicians.
What is a generalized mean-curvature flow? Notices of the American Mathematical Society 64 (2017), 580-581.