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  3. Aspects of Sobolev-Type Inequalities
  • Cited by 99
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      November 2001
      ISBN:
      9780511549762
      9780521006071
      DOI:
      https://doi.org/10.1017/CBO9780511549762
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.286kg, 202 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      London Mathematical Society Lecture Note Series (289)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    London Mathematical Society Lecture Note Series (289)
    Information

    Book description

    This book, first published in 2001, focuses on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincaré and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincaré's inequality on the other. It is suitable to be used as an advanced graduate textbook and will also be a useful source of information for graduate students and researchers in analysis on manifolds, geometric differential equations, Brownian motion and diffusion on manifolds, as well as other related areas.

    Reviews

    ‘The book is very well written and organized. it contains so many comments and explanations that both experts and non-experts on the subject may enjoy reading it.’

    Source: Zentralblatt für Mathematik

    '… a well-written and self-contained account of the topic.'

    Source: EMS Newsletter

    '[This book] constitues a valuable addition to the modern theory of inequalities.'

    Source: Bulletin of the Belgian Mathematical Society

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