Abstract
We investigate the behavior of Hardy constants in domains whose boundaries have at least one regular point.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. L. Sobolev, Selected Topics in the Theory of Functional Spaces and Generalized Functions (Nauka, Moscow, 1989) [in Russian].
V. G. Maz’ya, Sobolev Spaces (Springer, Berlin-New York, 1985).
T. Matskewich and P. E. Sobolevskii, “The Best Possible Constant in a Generalized Hardy’s Inequality for Convex Domains in Rn,” Nonlinear Anal. 28, 1601–1610 (1997).
M. Marcus, V. J. Mitzel, and Y. Pinchover, “On the BestConstant for Hardy’s Inequality inRn,” Trans. Amer. Math. Soc. 350, 3237–3250 (1998).
F. G. Avkhadiev, “Hardy Type Inequalities in Higher Dimensions with Explicit Estimate of Constants,” Lobachevskii J. Math. 21 (2006), 3–31 (2006).
F. G. Avkhadiev, “Hardy Type Inequalities in Planar and Spatial Open Sets,” Trudy Matem. Inst. im. V. A.Steklova 255, 8–18 (2006).
E. B. Davies, “The Hardy Constant,” Quart. J. Math. Oxford (2), 46 (4), 417–431 (1995).
V. M. Miklyukov and M. Vuorinen, “Hardy’s Inequality for W 1,p0 -Functions on Riemannian Manifolds,” Proc. Amer. Math. Soc. 127 (9), 2245–2254 (1999).
F.G. Avkhadiev and K.-J. Wirths, “Unified Poincaré and Hardy Inequalities with Sharp Constants for Convex Domains,” Z. Angew. Math. Mech. 87 (8–9), 632–642 (2007).
F. G. Avkhadiev and K.-J. Wirths, “Weighted Hardy Inequalities with Sharp Constants,” Lobachevskii J. Math. 31 (1), 1–7 (2010).
F. G. Avkhadiev and K.-J. Wirths, “Sharp Hardy-Type Inequalities with Lamb’s Constants,” Bull. Belg. Math. Soc. Simon Stevin 18, 723–736 (2011).
F. G. Avkhadiev and K.-J. Wirths, “On the Best Constants for the Brezis-Marcus Inequalities in Balls,” J. Math. Anal. and Appl. 396 (2), 472–480 (2012).
F. G. Avkhadiev, “Families of Domains with Best Possible Hardy Constant,” Izv. Vyssh. Uchebn. Zaved. MAt., No. 9, 59–63 (2013) [Russian Mathematics (Iz. VUZ) 57 (9), 49–52 (2013)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © F.G. Avkhadiev and I.K. Shafigullin, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 2, pp. 69–73.
About this article
Cite this article
Avkhadiev, F.G., Shafigullin, I.K. Sharp estimates of Hardy constants for domains with special boundary properties. Russ Math. 58, 58–61 (2014). https://doi.org/10.3103/S1066369X14020091
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X14020091