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Sharp estimates of Hardy constants for domains with special boundary properties

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Abstract

We investigate the behavior of Hardy constants in domains whose boundaries have at least one regular point.

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References

  1. S. L. Sobolev, Selected Topics in the Theory of Functional Spaces and Generalized Functions (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  2. V. G. Maz’ya, Sobolev Spaces (Springer, Berlin-New York, 1985).

    Google Scholar 

  3. 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).

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Marcus, V. J. Mitzel, and Y. Pinchover, “On the BestConstant for Hardy’s Inequality inRn,” Trans. Amer. Math. Soc. 350, 3237–3250 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  5. F. G. Avkhadiev, “Hardy Type Inequalities in Higher Dimensions with Explicit Estimate of Constants,” Lobachevskii J. Math. 21 (2006), 3–31 (2006).

    MATH  MathSciNet  Google Scholar 

  6. F. G. Avkhadiev, “Hardy Type Inequalities in Planar and Spatial Open Sets,” Trudy Matem. Inst. im. V. A.Steklova 255, 8–18 (2006).

    MathSciNet  Google Scholar 

  7. E. B. Davies, “The Hardy Constant,” Quart. J. Math. Oxford (2), 46 (4), 417–431 (1995).

    Article  MATH  Google Scholar 

  8. 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).

    Article  MathSciNet  Google Scholar 

  9. 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).

    Article  MATH  MathSciNet  Google Scholar 

  10. F. G. Avkhadiev and K.-J. Wirths, “Weighted Hardy Inequalities with Sharp Constants,” Lobachevskii J. Math. 31 (1), 1–7 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  11. 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).

    MATH  MathSciNet  Google Scholar 

  12. 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).

    Article  MathSciNet  Google Scholar 

  13. 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)].

    Google Scholar 

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    F. G. Avkhadiev & I. K. Shafigullin

Authors
  1. F. G. Avkhadiev
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  2. I. K. Shafigullin
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Correspondence to F. G. Avkhadiev.

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.

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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

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  • DOI: https://doi.org/10.3103/S1066369X14020091

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