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MiS Preprint
82/2013

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

Armin Schikorra

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.

Received:
Aug 15, 2013
Published:
Aug 16, 2013
MSC Codes:
49Q15, 46E35
Keywords:
Zero Sets, Fractional Sobolev Space

Related publications

inJournal
2015 Repository Open Access
Armin Schikorra

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

In: Proceedings of the American Mathematical Society, 142 (2015), pp. 1189-1197