Minimizing sequences of Sobolev inequalities revisited
Analysis of PDEs
2025-06-12 v2 Mathematical Physics
math.MP
Abstract
We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement of the Sobolev embedding theorem.
Keywords
Cite
@article{arxiv.2412.08616,
title = {Minimizing sequences of Sobolev inequalities revisited},
author = {Charlotte Dietze and Phan Thành Nam},
journal= {arXiv preprint arXiv:2412.08616},
year = {2025}
}
Comments
12 pages, final version to appear in IMRN