Geodesic
Sharp estimates of Hardy constants for domains with special boundary properties
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 69-73.

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We investigate the behavior of Hardy constants in domains whose boundaries have at least one regular boundary point.
Keywords: Hardy inequalities, distance function, Hardy constants. 
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F. G. Avkhadiev; I. K. Shafigullin. Sharp estimates of Hardy constants for domains with special boundary properties. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 69-73. http://geodesic.mathdoc.fr/item/IVM_2014_2_a8/

[1] Sobolev S. L., Izbrannye voprosy teorii funktsionalnykh prostranstv i obobschennykh funktsii, Nauka, M., 1989 | MR

[2] Maz'ya V. G., Sobolev spaces, Springer, Berlin–New York, 1985 | MR

[3] Matskewich T., Sobolevskii P. E., “The best possible constant in a generalized Hardy's inequality for convex domains in $\mathbb R^n$”, Nonlinear Anal., 28 (1997), 1601–1610 | DOI | MR | Zbl

[4] Marcus M., Mitzel V. J., Pinchover Y., “On the best constant for Hardy's inequality in $\mathbb R^n$”, Trans. Amer. Math. Soc., 350 (1998), 3237–3250 | DOI | MR

[5] Avkhadiev F. G., “Hardy type inequalities in higher dimensions with explicit estimate of constants”, Lobachevskii J. Math., 21 (2006), 3–31 | MR | Zbl

[6] Avkhadiev F. G., “Neravenstva tipa Khardi v ploskikh i prostranstvennykh otkrytykh mnozhestvakh”, Tr. matem. inst. im. V. A. Steklova, 255, 2006, 8–18 | MR

[7] Davies E. B., “The Hardy constant”, Quart. J. Math. Oxford (2), 46:4 (1995), 417–431 | DOI | MR | Zbl

[8] Miklyukov V. M., Vuorinen M., “Hardy's inequality for $W_0^{1,p}$-functions on Riemannian manifolds”, Proc. Amer. Math. Soc., 127:9 (1999), 2245–2254 | DOI | MR

[9] Avkhadiev F. G., Wirths K.-J., “Unified Poincaré and Hardy inequalities with sharp constants for convex domains”, Z. Angew. Math. Mech. (ZAMM), 87:8–9 (2007), 632–642 | DOI | MR | Zbl

[10] Avkhadiev F. G., Wirths K.-J., “Weighted Hardy inequalities with sharp constants”, Lobachevskii J. Math., 31:1 (2010), 1–7 | DOI | MR | Zbl

[11] Avkhadiev F. G., Wirths K.-J., “Sharp Hardy-type inequalities with Lamb's constants”, Bull. Belg. Math. Soc. Simon Stevin, 18 (2011), 723–736 | MR | Zbl

[12] Avkhadiev F. G., Wirths K.-J., “On the best constants for the Brezis–Marcus inequalities in balls”, J. Math. Anal. and Appl., 396:2 (2012), 472–480 | DOI | MR

[13] Avkhadiev F. G., “Semeistva oblastei, obladayuschikh maksimalnoi konstantoi Khardi”, Izv. vuzov. Matem., 2013, no. 9, 59–63