Short proofs of refined sharp Caffarelli-Kohn-Nirenberg inequalities
Analysis of PDEs
2021-12-01 v1 Functional Analysis
Abstract
This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained proofs. Our results are sharp and minimizers are obtained in suitable functional spaces. As main tools we use the so-called \textit{expand of squares} method to establish sharp weighted -Caffarelli-Kohn-Nirenberg (CKN) inequalities and density arguments.
Keywords
Cite
@article{arxiv.2104.10372,
title = {Short proofs of refined sharp Caffarelli-Kohn-Nirenberg inequalities},
author = {Cristian Cazacu and Joshua Flynn and Nguyen Lam},
journal= {arXiv preprint arXiv:2104.10372},
year = {2021}
}
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13 pages