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A Remark on Isolated Singularities at the Free Boundary of Harmonic Maps

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Abstract

Using a simple lemma on harmonic functions it is shown how well known results can be combined to exclude isolated singularities at the free boundary of two-dimensional weakly harmonic maps.

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References

  1. Courant, R.: Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces. Interscience, New York (1950). Reprint: Springer-Verlag, New York/Heidelberg/Berlin, 1977.

    Google Scholar 

  2. Dierkes, U., Hildebrandt, S., Küster, A. and Wohlrab, O.: Minimal Surfaces I. Grundlehren math. Wiss., Vol. 295. Springer-Verlag, Berlin/Heidelberg, 1992.

    Google Scholar 

  3. Dierkes, U., Hildebrandt, S., Küster, A. and Wohlrab, O.: Minimal Surfaces II. Grundlehren math. Wiss., Vol. 296. Springer-Verlag, Berlin/Heidelberg, 1992.

    Google Scholar 

  4. Duzaar, F. and Grotowski, J. F.: A mixed boundary value problem for energy minimizing harmonic maps, Math. Z. 221 (1996), 153-167.

    Google Scholar 

  5. Duzaar, F. and Steffen, K.: A partial regularity theorem for harmonic maps at a free boundary, Asymptotic Analysis 2 (1989), 299-343.

    Google Scholar 

  6. Dziuk, G.: C 2-Regularity for partially free minimal surfaces, Math. Z. 189 (1985), 71-79.

    Google Scholar 

  7. Grüter, M.: Conformally invariant variational integrals and the removability of isolated singularities, Manuscr. Math. 47 (1984), 85-104.

    Google Scholar 

  8. Grüter, M.: Regularity at the free boundary of two-dimensional stationary harmonic maps. Preprint no. 446, SFB 256, Bonn, 1995. To appear in: Analyse non linéaire (1997).

  9. Grüter, M., Hildebrandt, S. and Nitsche, J. C. C.: On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area, Manuscr. Math. 35 (1981), 387-410.

    Google Scholar 

  10. Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. II. Freie Ränder, Arch. Ration. Mech. Anal. 39 (1970), 275-293.

    Google Scholar 

  11. Jäger, W.: Behavior of minimal surfaces with free boundaries, Commun. Pure Appl. Math. 23 (1970), 803-818.

    Google Scholar 

  12. Sacks, J. and Uhlenbeck, K.: The existence of minimal immersions of two-spheres, Ann. Math. 113 (1981), 1-24.

    Google Scholar 

  13. Tomi, F.: Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme, Math. Z. 112 (1969), 214-218.

    Google Scholar 

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  1. Universitäat des Saarlandes, Im Stadtwald, D-66123, Saarbrüucken, Germany

    Michael Grüter (Fachbereich Mathematik)

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  1. Michael Grüter
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Grüter, M. A Remark on Isolated Singularities at the Free Boundary of Harmonic Maps. Annals of Global Analysis and Geometry 15, 173–178 (1997). https://doi.org/10.1023/A:1006517314129

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