A sharp analog of Young's inequality on S N and related entropy inequalities

E. A. Carlen, E. H. Lieb, M. Loss

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

We prove a sharp analog of Young's inequality on S N, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This strategy also works for the generalization of Young's inequality on R N to more than three functions, and leads to significant new information about the optimizers and the constants.

Original languageEnglish (US)
Pages (from-to)487-520
Number of pages34
JournalJournal of Geometric Analysis
Volume14
Issue number3
DOIs
StatePublished - Dec 1 2004

Fingerprint

Young's Inequality
Entropy Inequality
Analogue
Sharp Inequality
Heat Flow
Monotonic
Deduce
Strategy
Generalization

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Inequalities
  • best constants
  • entropy
  • optimizers

Cite this

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A sharp analog of Young's inequality on S N and related entropy inequalities. / Carlen, E. A.; Lieb, E. H.; Loss, M.

In: Journal of Geometric Analysis, Vol. 14, No. 3, 01.12.2004, p. 487-520.

Research output: Contribution to journalArticle

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