Equadiff 6 pp 215-219 | Cite as

Partial regularity of minimizers

  • M. Giaquinta
Lectures Presented In Sections Section B Partial Differential Equations
Part of the Lecture Notes in Mathematics book series (LNM, volume 1192)


Riemannian Manifold Hausdorff Dimension Partial Regularity Quasilinear System Target Manifold 
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  1. [1]
    Baldes, A., Stability and Uniqueness Properties of the Equator Map from a Ball into an Ellipsoid, Math. Z. 185 (1984), 505–516.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    EELLS, J., Lemaire, L., A report on harmonic maps, Bull. London Math. Soc. 10 (1878), 1–68.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    EELLS,J., Lemaire,L., Selected topics in harmonic maps, CBMS Regional Conference series.Google Scholar
  4. [4]
    EELLS, J., Sampson, J.H., Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Evans,C.L., Quasiconvexity and partial regularity in the calculus of variations, preprint 1984.Google Scholar
  6. [6]
    Giaquinta, M., A counterexample to the boundary regularity of solutions to elliptic quasilinear systems, manuscripta math. 14 (1978), 217–220.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Giaquinta,M., Multiple integrals in the Calculus of Vaniations and non linear elliptic systems, Annals. Math. Studies n° 105, Princeton University Press, 1983.Google Scholar
  8. [8]
    Giaquinta, M., Giusti, E., On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31–46.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Giaquinta, M., Giusti, E., Differentiability of minima of non differentiable functionals, Inventiones Math. 72 (1983), 285–298.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Giaquinta, M., Giusti, E., The singular set of the minima of certain quadratic functionals, Ann.Sc.Norm.Sup. Pisa 11 (1984), 45–55.MathSciNetzbMATHGoogle Scholar
  11. [11]
    Giaquinta,M., Ivert,P.A., Partial regularity for minima of variational integrals, Arkiv för Math.Google Scholar
  12. [12]
    Giaquinta,M., Modica,G., Partial regularity of minimizers of quasiconvex integrals, Ann. Inst. H. Poincaré, Analyse non linéaire.Google Scholar
  13. [13]
    Giaquinta,M., Souček,J., Harmonic maps into a hemisphere, Ann. Sc. Norm. Sup. Pisa.Google Scholar
  14. [14]
    Giaquinta, M., Souček, J., Cacciopoli's inequality and Legendre-Hadamard condition, Math. Ann. 270 (1985), 105–107.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Hildebrandt, S., Kaul, H., Widman, K.O., An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math. 138 (1977), 1–16.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Jäger, W., Kaul, H., Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems, J. reine u. angew. Math. 343 (1983), 146–161.MathSciNetzbMATHGoogle Scholar
  17. [17]
    Jost,J., Harmonic mappings between Riemannian manifolds, Centre for Math. Anal., Australian National Univ., vol. 4, 1983.Google Scholar
  18. [18]
    Jost, J., Meier, M., Boundary regularity for minima of certain quadratic functionals, Math. Ann. 262 (1983), 549–561.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Schoen, R., Uhlenbeck, K., A regularity theory for harmonic maps, J. Diff. Geom. 17 (1982), 307–335.MathSciNetzbMATHGoogle Scholar
  20. [20]
    Schoen, R., Uhlenbeck, K., Boundary regularity and miscellaneous results on harmonic maps, J. Diff. Geom. 18 (1983), 253–268.MathSciNetzbMATHGoogle Scholar
  21. [21]
    Schoen,R., Uhlenbeck,K., Regularity of minimizing harmonic maps into the sphere, Inventiones math.Google Scholar
  22. [22]
    Uhlenbeck, K., Regularity for a class of nonlinear elliptic systems, Acta Math. 138 (1977), 219–240.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Equadiff 6 and Springer-Verlag 1986

Authors and Affiliations

  • M. Giaquinta
    • 1
  1. 1.Instituto di Matematica ApplicataUniversita di FirenzeFirenzeItaly

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