A note on zero sets of fractional sobolev functions with negative power of integrability
Analysis of PDEs
2013-07-22 v1
Abstract
We extend a Poincar\'{e}-type inequality for functions with large zero-sets by Jiang and Lin to fractional Sobolev spaces. As a consequence, we obtain a Hausdorff dimension estimate on the size of zero sets for fractional Sobolev functions whose inverse is integrable. Also, for a suboptimal Hausdorff dimension estimate, we give a completely elementary proof based on a pointwise Poincar\'{e}-style inequality.
Keywords
Cite
@article{arxiv.1307.5236,
title = {A note on zero sets of fractional sobolev functions with negative power of integrability},
author = {Armin Schikorra},
journal= {arXiv preprint arXiv:1307.5236},
year = {2013}
}