Hardy inequalities for simply connected planar domains

Research paper by Ari Laptev, Alexander V. Sobolev

Indexed on: 15 Mar '06Published on: 15 Mar '06Published in: Mathematics - Functional Analysis

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.