Regularity Theory for Elliptic Partial Differential Equations
University of Coimbra
Institution: University of Texas in Austin
Year: 2013
I work on elliptic and parabolic partial differential equations, more specifically in the analysis and regularity aspects of these equations. My contributions also include analysis of integro-differential operators, free boundary problems and calculus of variations. In my research I have developed estimates for solutions of differential equations based on classic geometric ideas such as maximum principles, Harnack's inequalities and regularity by compactness. The fundamental questions and insights for these problems are motivated in physical and social sciences, probability, geometry and optimization.
