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arXiv · 1305.4616

Fractional Hardy inequalities and visibility of the boundary

Lizaveta Ihnatsyeva·Juha Lehrbäck·Heli Tuominen·Antti V. Vähäkangas
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Abstract

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.

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Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas. 2013-05-20. Fractional Hardy inequalities and visibility of the boundary. https://doi.org/10.4064/sm224-1-3

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