Attainability of the best Sobolev constant in a ball
Functional Analysis
2018-07-04 v2 Analysis of PDEs
Abstract
The best constant of the Sobolev inequality in the whole space is attained by the Aubin-Talenti function; however, this does not happen in bounded domains because the break in dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin-Talenti type. Generalization to the Caffarelli-Kohn-Nirenberg inequality in a ball is also discussed.
Keywords
Cite
@article{arxiv.1807.00127,
title = {Attainability of the best Sobolev constant in a ball},
author = {Norisuke Ioku},
journal= {arXiv preprint arXiv:1807.00127},
year = {2018}
}
Comments
16 pages