Rearrangement methods in the work of Elliott Lieb
History and Overview
2022-07-13 v1 Mathematical Physics
Analysis of PDEs
Functional Analysis
math.MP
Abstract
We review some topics in the theory of symmetric decreasing rearrangements with a particular focus on Lieb's fundamental contributions. Topics covered include the Brascamp--Lieb--Luttinger theorem, the sharp Young and Hardy--Littlewood--Sobolev inequalities, as well as the continuity of the rearrangement map on Sobolev spaces.
Keywords
Cite
@article{arxiv.2207.05153,
title = {Rearrangement methods in the work of Elliott Lieb},
author = {Rupert L. Frank},
journal= {arXiv preprint arXiv:2207.05153},
year = {2022}
}
Comments
22 pages; Dedicated, in great admiration, to Elliott Lieb on the occasion of his 90th birthday