Minimizers for the fractional Sobolev inequality on domains
Analysis of PDEs
2017-07-04 v1 Functional Analysis
Abstract
We consider a version of the fractional Sobolev inequality in domains and study whether the best constant in this inequality is attained. For the half-space and a large class of bounded domains we show that a minimizer exists, which is in contrast to the classical Sobolev inequalities in domains.
Keywords
Cite
@article{arxiv.1707.00131,
title = {Minimizers for the fractional Sobolev inequality on domains},
author = {Rupert L. Frank and Tianling Jin and Jingang Xiong},
journal= {arXiv preprint arXiv:1707.00131},
year = {2017}
}
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35 pages