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

Armin Schikorra

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arXiv · 1307.5236

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

Armin Schikorra

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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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Armin Schikorra. 2013-07-19. A note on zero sets of fractional sobolev functions with negative power of integrability. https://arxiv.org/abs/1307.5236

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