On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation

Herm Jan Brascamp, Elliott H. Lieb

Research output: Contribution to journalArticle

462 Scopus citations

Abstract

We extend the Prékopa-Leindler theorem to other types of convex combinations of two positive functions and we strengthen the Prékopa-Leindler and Brunn-Minkowski theorems by introducing the notion of essential addition. Our proof of the Prékopa-Leindler theorem is simpler than the original one. We sharpen the inequality that the marginal of a log concave function is log concave, and we prove various moment inequalities for such functions. Finally, we use these results to derive inequalities for the fundamental solution of the diffusion equation with a convex potential.

Original languageEnglish (US)
Pages (from-to)366-389
Number of pages24
JournalJournal of Functional Analysis
Volume22
Issue number4
DOIs
StatePublished - Aug 1976

All Science Journal Classification (ASJC) codes

  • Analysis

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