Improved Sobolev inequality under constraints
Classical Analysis and ODEs
2021-02-26 v2 Differential Geometry
Abstract
We give a new proof of Aubin's improvement of the Sobolev inequality on under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on , we determine the constant explicitly in the second order moments case.
Cite
@article{arxiv.2010.10654,
title = {Improved Sobolev inequality under constraints},
author = {Fengbo Hang and Xiaodong Wang},
journal= {arXiv preprint arXiv:2010.10654},
year = {2021}
}
Comments
25 pages. Typos corrected, references added, to appear in IMRN