Analysis and Partial Differential Equations

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.


Beatrous' Research
Beatrous' research is primarily in several complex variables and secondarily in harmonic and functional analysis.
Hajlasz’s Research
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.
Lennard's Research
Banach space geometry and metric fixed point theory.
Lewicka's Research
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's Research
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
Pakzad's research concerns nonconvex calculus of variations and geometric analysis.
Pan's Research
Pan's main research area is harmonic analysis.
Rabier's Research
Rabier's interests are in functional analysis, PDEs, ODEs, and numerical analysis (in that order).


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