Héctor A. Chang-Lara
Department of Mathematics
Office: Math 415
Office hours: Fridays 10-noon
Phone: (212) 854-4354
E-Mail: changlara at math dot columbia dot edu
My current research focuses on elliptic and parabolic integro-differential problems. In recent years this area has seen an increased number of publications with tools ranging from probability to analysis. My contributions belong to the analytical perspective but I am also very interested in learning new techniques. I wrote my PhD thesis on 2013 at the University of Texas in Austin under the supervision of Luis Caffarelli. I have worked on regularity estimates for viscosity solutions of fully nonlinear integro-differential parabolic equations, variational problems involving free boundaries and asymptotic shape theorems for queueing models.
Publications and preprints (arXiv, MathSciNet)
- with Nestor Guillén From the free boundary condition for Hele-Shaw to a fractional parabolic equation.
- 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 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).
- Regularity for fully non linear equations with non local drift.
- 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).