Equivalence of Sobolev inequalities and Lieb–Thirring inequalities

Rupert L. Frank, Elliott H. Lieb, Robert Seiringer

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Scopus citations

Abstract

We show that, under very general definitions of a kinetic energy operator T, the Lieb– Thirring inequalities for sums of eigenvalues of T − V can be derived from the Sobolev inequality appropriate to that choice of T.

Original languageEnglish (US)
Title of host publicationXVIth International Congress on Mathematical Physics
PublisherWorld Scientific Publishing Co.
Pages523-535
Number of pages13
ISBN (Electronic)9789814304634
ISBN (Print)981430462X, 9789814304627
DOIs
StatePublished - Jan 1 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

Keywords

  • Bound states
  • Schrödinger operator
  • Sobolev inequality
  • Stability of matter

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  • Cite this

    Frank, R. L., Lieb, E. H., & Seiringer, R. (2010). Equivalence of Sobolev inequalities and Lieb–Thirring inequalities. In XVIth International Congress on Mathematical Physics (pp. 523-535). World Scientific Publishing Co.. https://doi.org/10.1142/9789814304634_0045