Geodesic
Hardy type inequalities for a special family of non-convex domains
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 1, pp. 211-220

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In this work, we obtain Hardy type inequalities that involve the distance to the boundary and the volume of a domain for a special family of non-convex domains. These inequalities are analogues of the inequalities for convex domains proved by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, and J. Tidblom. To prove Hardy type inequalities, we propose a sufficient condition of regularity for multidimensional domains. Hardy type inequalities for certain non-convex domains in two- and three-dimensional spaces are used as an example.
Keywords: Hardy type inequalities, regular domains.
Mots-clés : convex domains 
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     title = {Hardy type inequalities for a~special family of non-convex domains},
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A. M. Tukhvatullina. Hardy type inequalities for a special family of non-convex domains. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 1, pp. 211-220. http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a16/