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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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Selected new aspects of the calculus of variations in the large
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by Ivar Ekeland and Nassif Ghoussoub PDF
Bull. Amer. Math. Soc. 39 (2002), 207-265 Request permission

Abstract:

We discuss some of the recent developments in variational methods while emphasizing new applications to nonlinear problems. We touch on several issues: (i) the formulation of variational set-ups which provide more information on the location of critical points and therefore on the qualitative properties of the solutions of corresponding Euler-Lagrange equations; (ii) the relationships between the energy of variationally generated solutions, their Morse indices, and the Hausdorff measure of their nodal sets; (iii) the gluing of several topological obstructions; (iv) the preservation of critical levels after deformation of functionals; (v) and the various ways to recover compactness in certain borderline variational problems.
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Additional Information
  • Ivar Ekeland
  • Affiliation: CEREMADE, Université Paris-Dauphine, Paris, France
  • MR Author ID: 62405
  • Email: Ivar.Ekeland@dauphine.fr
  • Nassif Ghoussoub
  • Affiliation: Pacific Institute for the Mathematical Sciences, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2
  • MR Author ID: 73130
  • Email: nassif@math.ubc.ca
  • Received by editor(s): January 20, 2001
  • Received by editor(s) in revised form: June 13, 2001
  • Published electronically: January 4, 2002
  • Additional Notes: The second author was partially supported by a grant from the Natural Science and Engineering Research Council of Canada (NSERC)
  • © Copyright 2002 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 39 (2002), 207-265
  • MSC (2000): Primary 35J60, 47J30, 58E05; Secondary 57R17
  • DOI: https://doi.org/10.1090/S0273-0979-02-00929-1
  • MathSciNet review: 1886088