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On the Behavior of the Derivatives of Minimizers near Singular Points

  • Enrico Giusti

Abstract

In spite of its relevance to the calculus of variations, the regularity of minimizers of variational integrals as such (i.e. as opposed to stationary points) has been studied only recently in [2]. Since then, several papers dedicated to the study of that problem have appeared.

Keywords

Singular Point Elliptic System Minimal Hypersurface Regularity Theorem Nonlinear Elliptic System 
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References

  1. 1.
    Giaquinta, M. Multiple integrals in the calculus of variations and nonlinear elliptic systems. Annals of Math. Studies 105. Princeton Univ. Press 1983.Google Scholar
  2. 2.
    Giaquinta, M., & E. Giusti, On the regularity of the minima of variational integrals.Acta Math 148 (1982) 31–46MATHMathSciNetGoogle Scholar
  3. 3.
    Giaquinta, M., & E. Giusti, The singular set of the minima of certain quadratic functionals. Ann. Sc. Norm. Sup. Pisa 11 (1984) 45–55.MATHMathSciNetGoogle Scholar
  4. 4.
    Giaquinta, M., & J. Soucek, Harmonic maps into a hemisphere. To appear in Ann. Sc. Norm. Sup. Pisa.11(1984)45–55Google Scholar
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    Giusti, E., Minimal surfaces and functions of bounded variation. Birkhauser Boston. 1984.Google Scholar
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    Jager, W., & J. Kaul, Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems. J. Reine Angew. Math. 343 (1983) 146–161.MathSciNetGoogle Scholar
  7. 7.
    Schoen, R., & K. Uhlenbeck, Regularity of minimizing harmonic maps into the sphere. Invent. Math. 78 (1984) 89–100.CrossRefMATHADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Enrico Giusti
    • 1
  1. 1.Istituto Matematico U. DiniUniversità di FirenzeItaly

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