Tadeusz Iwaniec Research Details
The main theme of my research: Nonlinear Analysis and Geometric Function Theory, which includes the following topics:
- Linear and Nonlinear Elliptic PDEs
- * Very weak solutions
- * LP- regularity theory
- * Orlicz-Sobolev type estimates
- * Differential forms
- The Calculus of Variations
- * Weak convergence methods
- * Jacobian determinants and null Lagrangians
- * Polyconvex and quasiconvex functionals
- Deformations of Finite Distortion
- * Functions of one complex variable
- * Quasiregular mappings in Rn and the governing PDEs
- * Topological properties of weakly differentiable mappings between Riemannian manifolds
- Harmonic Analysis Methods
- * Singular integrals (sharp estimates)
- * Interpolation and nonlinear commutators
- * Hardy spaces
- Applications
- Such general topics intersect modern areas of applied mathematics; nonlinear elasticity, material science, microstructure of crystals and so forth.
- Synergistic Activities
- The research program reflects continued efforts to reach out to graduate students and young scholars, incorporating research into learning (international summer school lectures) and partnerships (joint projects).
