Research articles: (arXiv, MathSciNet)
Publications
- Well-posedness for a transmission problem connecting first and second-order operators. (ESAIM: COCV)
- with Alberto Saldaña Classical solutions to integral equations with zero order kernels. (Math. Ann.)
- with Makson Santos Hölder regularity for non-variational porous media type equations. (J. of Differential Equations).
- with Edgard Pimentel Non-convex Hamilton-Jacobi equations with gradient constraints. (Nonlinear Analysis - Special Section on Recent developments in Free Boundary Problems)
- with Nestor Guillen and Russel Schwab Some free boundary problems recast as nonlocal parabolic equations. (Nonlinear Analysis).
- with Ovidiu Savin Boundary Regularity for the Free Boundary in the One-phase Problem. (Contemporary Mathematics - Proceedings of the Special Session).
- with Dennis Kriventsov Further Time Regularity for Non-Local, Fully Non-Linear Parabolic Equations. (CPAM).
- with Dennis Kriventsov Further time regularity for fully non-linear parabolic equations. (Math. Research Letters).
- with Gonzalo Dávila \(C^{2,\alpha}\) estimates for concave, non-local parabolic equations with critical drift. (J. of Integral Equations and Applications).
- with Gonzalo Dávila Hölder estimates for non-local parabolic equations with critical drift. (J. of Differential Equations).
- with François Baccelli and Sergey Foss Shape Theorems for Poisson Hail on a Bivariate Ground. (Advances in Applied Probability).
- with Mark Allen Free Boundaries on Two-Dimensional Cones. (J. of Geometric Analysis).
- with Gonzalo Dávila Regularity for solutions of nonlocal parabolic equations II. (J. of Differential Equations).
- with Gonzalo Dávila Regularity for solutions of non local parabolic equations. (Calculus of Variations and Partial Differential Equations).
- with Gonzalo Dávila Regularity for solutions of nonlocal, non symmetric equations. (Ann. Inst. H. Poincaré Anal. Non Linéaire).
Book Chapter
- A Visual Approach to the Regularity Theory for Fully Nonlinear Elliptic Equations. (Accepted in Modern Methods in the Analysis of Free Boundary Problems, Coimbra Mathematical Texts)
Expository
- A Perspective on the Regularity Theory of Degenerate Elliptic Equations. (Notices of the AMS)
- El problema del barrendero. (Revista Mixba'al)
See also the following implementation by José Joaquín Zubieta Rico and Karlo Jair Guevara Díaz (students at DEMAT, Universidad de Guanajuato):
https://suavesito-olimpiada.github.io/SweeperProblem/
Submitted preprints
- with Sergio Zapeta, A dynamic model of congestion.
- with Juan Carlos Fernandez and Alberto Saldaña, Fractional Q-curvature on the sphere and optimal partitions.