Absence of non-compactly supported minimisers for the Lieb-Oxford bound

Simone Di Marino; Rodrigue Lelotte

Absence of non-compactly supported minimisers for the Lieb-Oxford bound

Analysis of PDEs 2026-07-13 v1 Mathematical Physics

Authors: Simone Di Marino , Rodrigue Lelotte

Abstract

We prove the minimisers of the Lieb-Oxford bound (if any) for a fixed (and finite) number of particles $N \geq 1$ are necessarily compactly supported, extending a result proved by E. H. Lieb and S. Oxford in the one-particle case.

Keywords

Lieb-Oxford bound minimisers compactly supported density functional theory

Cite

@article{arxiv.2607.11440,
  title  = {Absence of non-compactly supported minimisers for the Lieb-Oxford bound},
  author = {Simone Di Marino and Rodrigue Lelotte},
  journal= {arXiv preprint arXiv:2607.11440},
  year   = {2026}
}