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Hardy Type Inequalities: Optimality and Minimizers
A seminar by Dr. Cristian Cazacu, Faculty of Mathematics and Computer Science, University of Bucharest, Romania. Dr. Cazacu's research focusses on Partial Differential Equations.
Abstract: In this exposure, we discuss both Hardy-Sobolev and Hardy-Rellich type inequalities. We focus on the best constants and the existence/nonexistence of minimizers. As a consequence, we establish useful properties for Schrodinger operators with singular potentials of the form P - aV, a > = 0, where P is a second-order differential operator (typically the Laplacian or the magnetic Laplacian) and V denotes (typically) a positive weight with quadratic singularities. Then we emphasize how such operators apply to study the well-posedness and the asymptotic behavior of some evolution PDEs with singular coefficients.