Harmonic Analysis and Partial Differential Equations

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Harmonic Analysis and Partial Differential EquationsProject AbstractCarlos E. KenigThe proposal will be a continuation of the PI's research on the regularity of solutions to free boundary problems, the analysis of boundary value problems under minimal smoothness conditions, the development of Liouville type theorems for viscous conservation laws, the development of techniques from Fourier analysis to study qualitative and quantitative properties of solutions of nonlinear dispersive equations and the use of quantitative unique continuation methods to study Anderson localization and the inverse problem in electrical impedance tomography. These partial differential equations arise in quantum mechanical models, fluid mechanics and tomography theory amongst other areas so the analysis of these equations may have many applications.