The Hardy and Caffarelli-Kohn-Nirenberg Inequalities Revisited
Aldo Bazan, Wladimir Neves
TL;DR
This paper revisits key inequalities in analysis, providing new proofs and insights into Hardy, Caffarelli-Kohn-Nirenberg, and Rellich inequalities, enhancing understanding of their structures and applications.
Contribution
It offers alternative proofs and detailed analysis of classical inequalities, including a new approach to Hardy's inequality and exploration of specific cases of Caffarelli-Kohn-Nirenberg's inequality.
Findings
New proof of Hardy's inequality using vector fields
Analysis of a particular case of Caffarelli-Kohn-Nirenberg's inequality
Study of Rellich's inequality with new insights
Abstract
In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of the Caffarelli-Kohn-Nirenberg's inequality. Finally, we study the Rellic's inequality.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Numerical methods in inverse problems