Rearrangement methods in the work of Elliott Lieb

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.

22 pages; Dedicated, in great admiration, to Elliott Lieb on the occasion of his 90th birthday