Skip to main content
Log in

Regularity of weakly harmonic maps from a surface into a manifold with symmetries

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [BC] H. BREZIS, J.-M. CORON,Multiple Solutions of H-Systems and Rellich's Conjecture, Comm. Pure Appl. Math.37 (1984), 149–187

    MATH  MathSciNet  Google Scholar 

  • [BK] H. BREZIS, T. KATO,Remarks on the Schrödinger Operator with Singular Complex Potentials, J. Math. Pures et Appl.58 (1979), 137–151

    MATH  MathSciNet  Google Scholar 

  • [BL] H. BREZIS, E.H. LIEB,Minimum Action Solutions of Some Vector Field Equations, Comm. Math. Phys.96 (1984), 97–113

    Article  MATH  MathSciNet  Google Scholar 

  • [CLMS] R.R. COIFMAN, P.-L. LIONS, Y. MEYER, S. SEMMES,Compacité par compensation et espaces de Hardy, C. R. Acad. Sci. Paris, t. 309, Série I (1989), 945–949

    MATH  MathSciNet  Google Scholar 

  • [Ch] Y.-M. CHEN,Weak Solutions to the Evolution Problems of Harmonic Maps, Math. Z

  • [Co] J.-M. CORON,private communication

  • [Gri] P. GRISVARD,Elliptic Problems in Non Smooth Domains, Monographs and Studies in Math.24, Pitman

  • [Grü] M. GRUETER,Regularity of weak H-Surfaces, J. Reine Angew. Math.329 (1981), 1–15

    MATH  MathSciNet  Google Scholar 

  • [H] F. HELEIN,Régularité des applications faiblement harmoniques entre une surface et une sphère, C. R. Acad. Sci. Paris Série I, t. 305

  • [HKW] S. HILDEBRANDT, H. KAUL, K.-O. WIDMANAn Existence Theorem for Harmonic Mappings of Riemannian Manifolds, Acta Math.138, (1977), 1–16

    Article  MATH  MathSciNet  Google Scholar 

  • [KRS] J. KELLER, J. RUBINSTEIN, P. STERNBERG,Reation-Diffusion Processes and Evolution to Harmonic Maps, Preprint

  • [LU] O. LADYZHENSKHAYA, N. URAL'TSEVA,Linear and Quasilinear Elliptic Equations, Academic Press New-York and London

  • [M] C. B. MORREY,The problem of Plateau on a Riemannian Manifold, Ann. of Math.49 (1948), 807–851

    Article  MathSciNet  Google Scholar 

  • C. B. MORREY,Multiple Integrals in the Calculus of Variations, Grundlehren 130 (Springer, Berlin 1966)

    MATH  Google Scholar 

  • [SU] J. SACKS, K. UHLENBECK,The Existence of Minimal Immersions of 2-Spheres, Ann. Math.113 (1981), 1–24

    Article  MathSciNet  Google Scholar 

  • [Sc] R. SCHOEN,Analytic Aspects of the Harmonic Maps Problem, Math. Sci. Res. Inst. Publ.2 (Springer, Berlin 1984), 321–358

    Google Scholar 

  • [Sh] J. SHATAH,Weak Solutions and Development of Singularities of the SU(2)-σmodel, Comm. Pure Appl. Math.41 (1988), 459–469

    MATH  MathSciNet  Google Scholar 

  • [T] S. TAKAKUWA,On Removable Singularities of Stationnary Harmonic Maps, J. of Fac. of Sciences, The University of Tokyo, Vol.32 (1985), 373–395

    MATH  MathSciNet  Google Scholar 

  • [W] H. WENTE,An Existence Theorem for Surfaces of Constant Mean Curvature, J. Math. Anal. Appl.26 (1969), 318–344

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by grant from D.R.E.T., D.G.A., France

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hélein, F. Regularity of weakly harmonic maps from a surface into a manifold with symmetries. Manuscripta Math 70, 203–218 (1991). https://doi.org/10.1007/BF02568371

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568371

Keywords

Navigation