A symmetry problem in the calculus of variations

  • F. Brock
  • V. Ferone
  • B. Kawohl
Article

DOI: 10.1007/BF01261764

Cite this article as:
Brock, F., Ferone, V. & Kawohl, B. Calc. Var (1996) 4: 593. doi:10.1007/BF01261764

Abstract

Let Ω be a ball in ℝN, centered at zero, and letu be a minimizer of the nonconvex functional\(R(v) = \int_\Omega {\tfrac{1}{{1 + |\nabla v(x)|^2 }}dx} \) over one of the classesCM := {wWloc1,∞() ∣ 0 ≤w(x) ≤M inΩ,w concave} orEM := {wWloc1,2 (Ω) ∣ 0 ≤w(x) ∖M in,Δw 0 inL′()}of admissible functions. Thenu is not radial and not unique. Therefore one can further reduce the resistance of Newton's rotational “body of minimal resistance“ through symmetry breaking.

Mathematics subject classification

49K2049N6035R3535B6535M10

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • F. Brock
    • 1
  • V. Ferone
    • 2
  • B. Kawohl
    • 1
  1. 1.Mathematisches Institut der Universität zu KölnKölnGermany
  2. 2.Dipartimento di MatematicaNapoliItaly