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A note on zero-sets of fractional sobolev functions with negative power of integrability

Author: Armin Schikorra
Journal: Proc. Amer. Math. Soc. 143 (2015), 1189-1197
MSC (2010): Primary 49Q15; Secondary 46E35
Published electronically: October 29, 2014
MathSciNet review: 3293734
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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.

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Additional Information

Armin Schikorra
Affiliation: Max-Planck Institut MiS Leipzig, Inselstr. 22, 04103 Leipzig, Germany

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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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