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, 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


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.


Recent Result Number Theory Algebraic Geometry Topological Group Minimal Cone 
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    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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