Equivalence of Sobolev inequalities and Lieb–Thirring inequalities

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

Research output: Chapter in Book/Report/Conference proceedingChapter

18 Scopus citations


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.
Number of pages13
ISBN (Electronic)9789814304634
ISBN (Print)981430462X, 9789814304627
StatePublished - Jan 1 2010

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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


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