CORDIS Project
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This project explores advanced mathematical methods to solve significant problems in vector calculus, imaging, and fluid mechanics. It focuses on quasiconformal mappings and their applications in various mathematical and physical contexts.
The use of delicate quasiconformal methods, in conjunction with convex integration and/or nonlinear Fourier analysis, will be the common theme of the proposal. A number of important outstanding problems are susceptible to attack via these methods.
First and foremost, Morrey's fundamental question in two dimensional vectorial calculus of variations will be considered as well as the related conjecture of Iwaniec regarding the sharp $L^p$ bounds for the Beurling transform.
Understanding the geom…
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