On Hardy and Caffarelli-Kohn-Nirenberg inequalities

2018/01/19 by Nguyen, Hoai-Minh, Squassina, Marco · 3 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1801.06329

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.

Cited by

• Radial symmetry of positive solutions to quasilinear Hardy-Sobolev doubly critical systems
• Characterizations of the Sobolev norms and the total variation via nonlocal functionals, and related problems
• Properties and applications of partial multiple weights for fractional integrals

Related

• The Hardy and Caffarelli-Kohn-Nirenberg Inequalities Revisited
• The Caffarelli-Kohn-Nirenberg Inequality for Submanifolds in Riemannian Manifolds
• A Caffarelli-Kohn-Nirenberg type inequality on Riemannian Manifolds
• Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for L^p-weighted Hardy inequalities
• Nonlocal Gagliardo-Nirenberg-Sobolev type inequality