In between the inequalities of Sobolev and Hardy
Classical Analysis and ODEs
2016-11-21 v1 Analysis of PDEs
Abstract
We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions.
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Cite
@article{arxiv.1502.01190,
title = {In between the inequalities of Sobolev and Hardy},
author = {Juha Lehrbäck and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:1502.01190},
year = {2016}
}
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27 pages