Sharp estimates of Hardy constants for domains with special boundary properties

被引：16
作者：
Avkhadiev F.G. [1 ]
Shafigullin I.K. [1 ]
机构：
[1] Kazan (Volga Region) Federal University, Kazan 420008
来源：
Russian Mathematics | 2014年 / 58卷 / 2期
基金：
俄罗斯基础研究基金会;
关键词：
and phrases: Hardy inequalities; distance function; Hardy constants;
D O I：
10.3103/S1066369X14020091
中图分类号：
学科分类号：
摘要：
We investigate the behavior of Hardy constants in domains whose boundaries have at least one regular point. © 2014 Allerton Press, Inc.
引用
收藏
页码：58 / 61
页数：3
相关论文
共 13 条
  • [1] Sobolev S.L., Selected Topics in the Theory of Functional Spaces and Generalized Functions, (1989)
  • [2] Maz'Ya V.G., Sobolev Spaces, (1985)
  • [3] Matskewich T., Sobolevskii P.E., The Best Possible Constant in a Generalized Hardy's Inequality for Convex Domains in R<sup>n</sup>, Nonlinear Anal., 28, pp. 1601-1610, (1997)
  • [4] Marcus M., Mitzel V.J., Pinchover Y., On the BestConstant for Hardy's Inequality inRn, Trans. Amer. Math. Soc., 350, pp. 3237-3250, (1998)
  • [5] Avkhadiev F.G., Hardy Type Inequalities in Higher Dimensions with Explicit Estimate of Constants, Lobachevskii J. Math., 21, 2006, pp. 3-31, (2006)
  • [6] Avkhadiev F.G., Hardy Type Inequalities in Planar and Spatial Open Sets, Trudy Matem. Inst. Im. V. A.Steklova, 255, pp. 8-18, (2006)
  • [7] Davies E.B., The Hardy Constant, Quart. J. Math. Oxford (2), 46, 4, pp. 417-431, (1995)
  • [8] Miklyukov V.M., Vuorinen M., Hardy's Inequality for W <sub>0</sub> <sup>1,p</sup> -Functions on Riemannian Manifolds, Proc. Amer. Math. Soc., 127, 9, pp. 2245-2254, (1999)
  • [9] Avkhadiev F.G., Wirths K.-J., Unified Poincaré and Hardy Inequalities with Sharp Constants for Convex Domains, Z. Angew. Math. Mech., 87, 8-9, pp. 632-642, (2007)
  • [10] Avkhadiev F.G., Wirths K.-J., Weighted Hardy Inequalities with Sharp Constants, Lobachevskii J. Math., 31, 1, pp. 1-7, (2010)
12