Geodesic
A geometric description of domains whose Hardy constant is equal to~1/4
Izvestiya. Mathematics , Tome 78 (2014) no. 5, pp. 855-876

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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 $f$ on the domain is greater than or equal to one quarter of the integral of $f^2(x)/\delta^2(x)$, where $\delta(x)$ is the distance from $x$ 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.
Keywords: Hardy inequalities, hypergeometric functions, torsional rigidity.
Mots-clés : non-convex domains 
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     author = {F. G. Avkhadiev},
     title = {A geometric description of domains whose {Hardy} constant is equal to~1/4},
     journal = {Izvestiya. Mathematics },
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F. G. Avkhadiev. A geometric description of domains whose Hardy constant is equal to~1/4. Izvestiya. Mathematics , Tome 78 (2014) no. 5, pp. 855-876. http://geodesic.mathdoc.fr/item/IM2_2014_78_5_a0/