Hardy inequalities for simply connected planar domains

Details Hardy inequalities for simply connected planar domains Hardy inequalities for simply connected planar domains

2006-03-15

arxiv.org/abs/math/0603362v1

Mathematics

Functional Analysis

9 pages

Scientific paper

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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