The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces.
Analysis and Partial Differential Equations
Beatrous' research is primarily in several complex variables and secondarily in harmonic and functional analysis.
Hajlasz’s research is focused on the theory of Sobolev spaces with applications to various areas like the theory of quasiconformal mappings, calculus of variations, regularity of nonlinear elliptic PDEs, and Carnot-Caratheodory spaces.
Banach space geometry and metric fixed point theory.
Lewicka's research areas are nonlinear analysis, partial differential equations and calculus of variations. She has obtained results on the well-posedness and stability of systems of conservation laws and reaction-diffusion equations.
Manfredi and his graduate students Robert Berry and Alexander Sviridov work on the p-Laplace equation, including p equals infinity, in Euclidean space and Carnot groups, and their connection with the Monge-Kantorovich mass transfer problem.
Pakzad's research concerns nonconvex calculus of variations and geometric analysis.