Equivalence of Sobolev inequalities and Lieb–Thirring inequalities

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

doi:10.1142/9789814304634_0045

Equivalence of Sobolev inequalities and Lieb–Thirring inequalities

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

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

19 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 language	English (US)
Title of host publication	XVIth International Congress on Mathematical Physics
Publisher	World Scientific Publishing Co.
Pages	523-535
Number of pages	13
ISBN (Electronic)	9789814304634
ISBN (Print)	981430462X, 9789814304627
DOIs	https://doi.org/10.1142/9789814304634_0045
State	Published - Jan 1 2010

All Science Journal Classification (ASJC) codes

General Mathematics
General Physics and Astronomy

Keywords

Bound states
Schrödinger operator
Sobolev inequality
Stability of matter

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10.1142/9789814304634_0045

Cite this

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title = "Equivalence of Sobolev inequalities and Lieb–Thirring inequalities",

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.",

keywords = "Bound states, Schr{\"o}dinger operator, Sobolev inequality, Stability of matter",

author = "Frank, {Rupert L.} and Lieb, {Elliott H.} and Robert Seiringer",

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AU - Frank, Rupert L.

AU - Lieb, Elliott H.

AU - Seiringer, Robert

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

KW - Bound states

KW - Schrödinger operator

KW - Sobolev inequality

KW - Stability of matter

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M3 - Chapter

AN - SCOPUS:84969628913

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SP - 523

EP - 535

BT - XVIth International Congress on Mathematical Physics

PB - World Scientific Publishing Co.

ER -

Equivalence of Sobolev inequalities and Lieb–Thirring inequalities

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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