We give a geometric description of families of non-convex planar and spatial domains in which the following Hardy inequality holds: the Dirichlet integral of any smooth compactly supported function on the domain is greater than or equal to one quarter of the integral of , where is the distance from to the boundary of the domain. Our geometric description is based analytically on new one-dimensional Hardy-type inequalities with special weights and on new constants related to these inequalities and hypergeometric functions.
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F. G. Avkhadiev (2014) studied this question.
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