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manuscripta mathematica

, Volume 63, Issue 2, pp 173–192 | Cite as

A classification of minimal cones in ℝn × ℝ+ and a counterexample to interior regularity of energy minimizing functions

  • Ulrich Dierkes
Article

Abstract

Recent results of the author concerning the minimizing properties of the cones\(C_n^\alpha = \left\{ {0 \leqslant x_{n + 1} \leqslant \sqrt {\frac{\alpha }{{n - 1}}[x_1^2 + ... + x_n^2 ]^{\frac{1}{2}} } } \right\}\) will be improved considerably. It is shown that the new results are optimal. Moreover the existence of “singular” minimizers of class C0,1/2 is established in any dimension n≥2.

Keywords

Recent Result Number Theory Algebraic Geometry Topological Group Minimal Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. [BD]
    Bemelmans, J., Dierkes, U.: On a singular variational integral with linear growth, I: existence and regularity of minimizers. Arch. Rat Mech. Anal.100 (1987), 83–103Google Scholar
  2. [D1]
    Dierkes, U.: Minimal hypercones and C0,1/2-minimizers for a singular variational problem. To appear in Indiana University Math. Journ.Google Scholar
  3. [D2]
    Dierkes, U.: Boundary regularity for solutions of a singular variational problem with linear growth. To appear in Arch. Rat. Mech. Anal.Google Scholar
  4. [S]
    Simoes, P.A.Q.: A class of minimal cones in ℝn, n≥8 that minimize area. Ph.D. thesis, University of California, Berkeley, CA 1973Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Ulrich Dierkes
    • 1
    • 2
  1. 1.Fachbereich MathematikUniversität des SaarlandesSaarbrücken
  2. 2.Sonderforschungsbereich 256Institut für Angewandte MathematikBonn 1

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