English

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 L2L^{2}-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