Hardy Inequalities for Simply Connected Planar Domains
نویسنده
چکیده
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. 1. Main result and discussion Let Ω be a domain in R and let Ω = R \ Ω be its complement. For any function u ∈ C10(Ω) we have: (1.1) ∫
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