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Isoperimetric inequalities on RN with respect to homogeneous weights

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DNM - The mathematical design of new materials

We solve a class of isoperimetric problems in the whole spacewith respect to monomial weights.  Our results imply that the optimizers  in some Caffarelli-Kohn-Nirenberg inequalities are radial. Further, they are used to obtain sharp apriori-bounds for solutions to some weighted elliptic BVPs.  \\ This is joint work with A. Alvino, F. Chiacchio and M.R. Posteraro (Napoli). 

This talk is part of the Isaac Newton Institute Seminar Series series.

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