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Hardy inequalities for simply connected planar domains

Ari Laptev·Alexander V. Sobolev
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Abstract

In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality.

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Ari Laptev, Alexander V. Sobolev. 2006-03-15. Hardy inequalities for simply connected planar domains. https://arxiv.org/abs/math/0603362

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