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Metastable Harmonic Maps

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Metastability and Incompletely Posed Problems

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 3))

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Abstract

The purpose of this lecture is to discuss a simple system with at least two distinct equilibrium states. The first state is an absolute minimum of the energy. The second state is a local minimum which exhibits some of the features of both stable and unstable equilibria.

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References

  1. H. Brezis, Some variational problems with lack of compactness, Proc. Symp. Nonlinear Functional Analysis, Berkeley, 1984, AMS.

    Google Scholar 

  2. H. Brezis — J.M. Coron, Multiple solutions of H-systems and Rellich’s conjecture, Comm. Pure Appl. Math. 37 (1984) p. 149–187.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Brezis — J.M. Coron, Large solutions for harmonic maps in two dimensions, Comm. Math. Phys. 92 (1983) p. 203–215.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. H. Brezis — J.M. Coron — E. Lieb, in preparation.

    Google Scholar 

  5. H. Brezis — L. Nirenberg, Positive solutions of nonlinear elliptic equations invoving critical Sobolev exponents, Comm. Pure. Appl. Math. 36 (1983) p. 433–477.

    Article  MathSciNet  Google Scholar 

  6. J.L. Ericksen — D. Kinderlehrer, eds., Proceedings of the IMA Workshop on the Theory and Applications of Liquid Crystals, Minneapolis, Jan. 1985.

    Google Scholar 

  7. M. Giaquinta — S. Hildebrandt, A priori estimates for harmonic map**s, J. Reine Angew. Math. 336 (1982) p. 124–164.

    Article  MathSciNet  Google Scholar 

  8. R. Hardt — D. Kinderlehrer — F.H. Lin, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys. (to appear).

    Google Scholar 

  9. R. Hardt — F.H. Lin in preparation.

    Google Scholar 

  10. J. Jost, The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values, J. Diff. Geom. 19 (1984) p. 393–401.

    MathSciNet  MATH  Google Scholar 

  11. L. Lemaire, Applications harmoniques de surfaces riemanniennes, J. Diff. Geom. 13 (1978) p. 51–78.

    MathSciNet  MATH  Google Scholar 

  12. L. Nirenberg, Topics in Nonlinear Functional Analysis, N.Y.U. Lecture Notes 1973–74.

    Google Scholar 

  13. R. Schoen — K. Uhlenbeck, Boundary regularity and miscellaneous results on harmonic maps, J. Diff. Geom. 18 (1983) p. 253–268.

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Département of Mathématiques, Université Paris VI, 4 Pl. Jussieu, 75230, Paris Cedex 05, France

    Haim Brezis

Authors
  1. Haim Brezis
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Stuart S. Antman

  2. School of Mathematics and Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, USA

    J. L. Ericksen

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    David Kinderlehrer

  4. FB9-Hermann Föttinger Institut, Technical University, Berlin, Germany

    Ingo Müller

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© 1987 Springer-Verlag New York Inc.

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Brezis, H. (1987). Metastable Harmonic Maps. In: Antman, S.S., Ericksen, J.L., Kinderlehrer, D., Müller, I. (eds) Metastability and Incompletely Posed Problems. The IMA Volumes in Mathematics and Its Applications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8704-6_3

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  • DOI: https://doi.org/10.1007/978-1-4613-8704-6_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8706-0

  • Online ISBN: 978-1-4613-8704-6

  • eBook Packages: Springer Book Archive

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