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