On the Hardy constant of some non-convex planar domains

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The Hardy constant of a simply connected domain Ω² is the best constant for the inequality ∫Ω|∇ u|²dx ≥ c∫Ω u² dist(x,∂Ω)² dx, u∈ C∞c(Ω). After the work of Ancona where the universal lower bound 1/16 was obtained, there has been a substantial interest on computing or estimating the Hardy constant of planar domains. In BT we have determined the Hardy constant of an arbitrary quadrilateral in the plane. In this work we continue our investigation and we compute the Hardy constant for other non-convex planar domains. In all cases the Hardy constant is related to that of a certain infinite sectorial region which has been studied by E.B. Davies.