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

Armin Schikorra

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Submission date: 15. Aug. 2013
Pages: 12
published in: Proceedings of the American Mathematical Society, 142 (2015), p. 1189-1197 
DOI number (of the published article): 10.1090/S0002-9939-2014-12372-0
Bibtex
MSC-Numbers: 49Q15, 46E35
Keywords and phrases: Zero Sets, Fractional Sobolev Space
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Abstract:
We extend a Poincare-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 Poincare-style inequality.