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  • 1
    Electronic Resource
    Electronic Resource
    A symmetry problem in the calculus of variations (1996)
    Springer
    Calculus of variations and partial differential equations 4 (1996), S. 593-599 
    Details
    ISSN: 1432-0835
    Keywords: 49K20 ; 49N60 ; 35R35 ; 35B65 ; 35M10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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 classesC M := {w ∈W loc 1,∞ (∖) ∣ 0 ≤w(x) ≤M inΩ,w concave} orE M := {w ∈W loc 1,2 (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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01261764
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