Title: A Non-variational Approach for the Porous Medium Equation

Abstract: We extend the Krylov-Safonov theory and the corresponding Hölder estimates for the viscosity solutions of a type porous medium equation with non-variational structure. Our method of proof combines ideas from harmonic analysis (Calderon Zygmund dyadic decomposition) and elliptic PDEs (diminish of oscillation). In collaboration with Makson Santos (University of São Paulo and Técnico Lisboa).

Article: https://arxiv.org/abs/2108.00464

About the Speaker: Hector Chang-Lara  received a BS in 2007 from Universidad Simón Bolívar, Caracas, Venezuela; a  MS from UNM in 2008, and a PhD from the  University of Texas at Austin in  in 2013 under the direction of Luis Cafferelli. Dr. Chang was a Ritt Assistant Professor at Columbia University (2013-2017) before joining the faculty at the Centro de Investigación en Matemáticas (CIMAT), Guanajuato, México. Chang works in partial differential equations,  specializing in elliptic and parabolic differential equations, more specifically in the analysis and regularity aspects of these equations.  Dr. Chang's contributions also include analysis of integro-differential operators, free boundary problems and calculus of variations.  Dr. Chang has mentored postdocs, graduate and undergraduate students. He has delivered many talks as well as minicourses in workshops in Europe, North  America and South America. He  has organized summer schools at CIMAT  and special sessions  in conferences. Dr. Chang has been Venezuela Team Leader at several recent Iberoamerican Mathematical Olympiads and an Observer for Venezuela at the 61th International Mathematical Olympiad (IMO) in St. Petersburg, Russia. Last but not least, Héctor represented Venezuela twice in the 42nd and 43rd IMO held in Washington D.C and Glasgow, Scotland in 2001 and 2002 obtaining in both Honorable Mentions.