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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). 


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