A note on zero-sets of fractional sobolev functions with negative power of integrability
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Abstract:
We extend a Poincaré-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 Poincaré-style inequality.References
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Additional Information
- Armin Schikorra
- Affiliation: Max-Planck Institut MiS Leipzig, Inselstr. 22, 04103 Leipzig, Germany
- MR Author ID: 880438
- Email: armin.schikorra@mis.mpg.de
- Received by editor(s): July 19, 2013
- Published electronically: October 29, 2014
- Additional Notes: The author was supported by DAAD fellowship D/12/40670
- Communicated by: Jeremy Tyson
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 1189-1197
- MSC (2010): Primary 49Q15; Secondary 46E35
- DOI: https://doi.org/10.1090/S0002-9939-2014-12372-0
- MathSciNet review: 3293734