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  3. An Introduction to Maximum Principles and Symmetry in Elliptic Problems
  • Cited by 131
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    • Publisher:
      Cambridge University Press
      Publication date:
      February 2010
      February 2000
      ISBN:
      9780511569203
      9780521461955
      9780521172783
      DOI:
      https://doi.org/10.1017/CBO9780511569203
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.615kg, 352 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.52kg, 352 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Real and Complex Analysis
      Series:
      Cambridge Tracts in Mathematics (128)
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Real and Complex Analysis
    Series:
    Cambridge Tracts in Mathematics (128)
    Information

    Book description

    Originally published in 2000, this was the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. Results are presented with minimal prerequisites in a style suited to graduate students. Two long and leisurely appendices give basic facts about the Laplace and Poisson equations. There is a plentiful supply of exercises, with detailed hints.

    Reviews

    Review of the hardback:'The originality of this book mainly consists in new proofs and new extensions of quite well known results concerning maximum principles and symmetry properties related to semilinear elliptic equations.'

    Source: Mathematical Reviews

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