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General sharp weighted Caffarelli–Kohn–Nirenberg inequalities

Part of: Linear function spaces and their duals Inequalities

Published online by Cambridge University Press:  27 December 2018

Nguyen Lam
Nguyen Lam*
Affiliation:
Department of Mathematics, University of British Columbia and The Pacific Institute for the Mathematical Sciences, Vancouver, BC V6T1Z4, Canada (nlam@math.ubc.ca)
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Abstract

In this paper, we will use optimal mass transport combining with suitable transforms to study the sharp constants and optimizers for a class of the Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities. Moreover, we will investigate these inequalities with and without the monomial weights $x_{1}^{A_{1}} \cdots x_{N}^{A_{N}}$ on ℝN.

Keywords

Gagliardo–Nirenberg inequalitiesCaffarelli–Kohn–Nirenberg inequalitiesbest constantsextremal functionsmass transportduality

MSC classification

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 3 , June 2019 , pp. 691 - 718
Copyright
Copyright © Royal Society of Edinburgh 2018 

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