Semiclassical Moser-Trudinger inequalities
Analysis of PDEs
2024-01-29 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.
Cite
@article{arxiv.2305.01456,
title = {Semiclassical Moser-Trudinger inequalities},
author = {Rakesh Arora and Phan Thành Nam and Phuoc-Tai Nguyen},
journal= {arXiv preprint arXiv:2305.01456},
year = {2024}
}
Comments
Final version to appear in Trans. Amer. Math. Soc., 18 pages