We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps from a sphere into itself and characterizations of Sobolev spaces.
Nguyen, H., Squassina, M., On Hardy and Caffarelli-Kohn-Nirenberg inequalities, <<JOURNAL D'ANALYSE MATHEMATIQUE>>, 2019; (275): 773-797. [doi:10.1007/s11854-025-0077-9] [http://hdl.handle.net/10807/132139]
On Hardy and Caffarelli-Kohn-Nirenberg inequalities
Squassina, Marco
Membro del Collaboration Group
2019
Abstract
We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps from a sphere into itself and characterizations of Sobolev spaces.
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