Semilinear Elliptic Differential Equations. Some Recent Results on Global Solutions

  • Philippe Blanchard
  • Erwin Brüning
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

All the results on concrete boundary and eigenvalue problems presented in Chaps. 6–8 use in an essential way at least one of the following two assumptions:
  1. 1.

    The domain G ⊂ℝd, over which the problem is considered, is bounded.

     
  2. 2.
    The exponents which are used to bound the nonlinearities are strictly smaller than the “critical Sobolev exponent” p* defined by
    $$\frac{1}{{p*}} = \frac{1}{p} - \frac{1}{d}{\text{ or }}p* = \frac{{dp}}{{d - p}}$$
    when one looks for solutions in W 1,p(G), 1 ≤ p < d.
     

Keywords

Manifold Covariance Assure Expense Convolution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Philippe Blanchard
    • 1
  • Erwin Brüning
    • 2
  1. 1.Theoretische Physik, Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa

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