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About the Hardy Inequality

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Abstract

The Hardy inequality has a long history and many variants. Together with the Sobolev inequalities, it is one of the most frequently used inequalities in analysis. In this note, we present some aspects of its history, as well as some of its extensions and applications. This is a very active research direction.

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References

  1. Lorenzo Giacomelli, Hans Knüpfer, and Felix Otto, Smooth zero-contact-angle solutions to a thin-film equation around the steady state. Journal of Differential Equations 245(6), 1454–1506 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Godfrey H. Hardy, Notes on some points in the integral calculus. XLI. On the convergence of certain integrals and series. Messenger of Mathematics 45, 163–166 (1915)

    Google Scholar 

  3. Godfrey H. Hardy, Notes on some points in the integral calculus. LX. An inequality between integrals. Messenger of Mathematics 54, 150–156 (1925)

    Google Scholar 

  4. Godfrey H. Hardy, John E. Littlewood, and George Pólya, Inequalities. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988); reprint of the 1952 edition

    MATH  Google Scholar 

  5. Juhi Jang and Nader Masmoudi, Well-posedness of compressible Euler equations in a physical vacuum. Preprint. http://arxiv.org/abs/1005.4441, 35 pages (May 24, 2010)

  6. Robert M. Kerr and Marcel Oliver, The ever-elusive blowup in the mathematical description of fluids. In: Dierk Schleicher and Malte Lackmann (editors), An Invitation to Mathematics: From Competitions to Research, pp. 137–164. Springer, Heidelberg (2011)

    Google Scholar 

  7. Alois Kufner, Lech Maligranda, and Lars-Erik Persson, The prehistory of the Hardy inequality. American Mathematical Monthly 113(8), 715–732 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Alois Kufner, Lech Maligranda, and Lars-Erik Persson, The Hardy inequality. About Its History and Some Related Results. Vydavatelský Servis, Plzeň (2007)

    MATH  Google Scholar 

  9. Nader Masmoudi, Well-posedness for the FENE dumbbell model of polymeric flows. Communications on Pure and Applied Mathematics 61(12), 1685–1714 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lloyd N. Trefethen, Ten digit problems. In: Dierk Schleicher and Malte Lackmann (editors), An Invitation to Mathematics: From Competitions to Research, pp. 119–136. Springer, Heidelberg (2011)

    Google Scholar 

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Correspondence to Nader Masmoudi .

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© 2011 Springer-Verlag Berlin Heidelberg

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Masmoudi, N. (2011). About the Hardy Inequality. In: Schleicher, D., Lackmann, M. (eds) An Invitation to Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19533-4_11

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