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4:00 pm Friday, October 31, 2008 Geometry-Analysis Seminar: The Sharp Constant in the Hardy-Sobolev-Maz'ya Inequalityby
Rupert Frank (Princeton University) in HB 227- We show that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional halfspace is given by the Sobolev constant on the whole space. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev-type inequality whose sharp constant is determined as well. We discuss an equivalent formulation in hyperbolic space and prove a similar result for the Moser-Trudinger inequality in two dimensions. The talk is based on joint work with R. Benguria and M. Loss.
Submitted by damanik@rice.edu |