English

A sharp monomial Caffarelli-Kohn-Nirenberg inequality

Analysis of PDEs 2026-01-28 v1

Abstract

We consider a monomial Caffarelli-Kohn-Nirenberg inequality, find the optimal constant and classify the optimizers under an integrated curvature dimension condition. We take advantage of the Γ\Gamma-calculus to exploit geometrical techniques to tackle the problem and regularity results to justify some integration by parts. A symmetry-breaking result is also provided.

Keywords

Cite

@article{arxiv.2601.19359,
  title  = {A sharp monomial Caffarelli-Kohn-Nirenberg inequality},
  author = {Francesco Pagliarin},
  journal= {arXiv preprint arXiv:2601.19359},
  year   = {2026}
}

Comments

34 pages

R2 v1 2026-07-01T09:21:53.810Z