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  • Springer  (3)
  • American Chemical Society
  • American Geophysical Union
  • 1995-1999  (3)
Collection
Keywords
Publisher
  • Springer  (3)
  • American Chemical Society
  • American Geophysical Union
Years
Year
  • 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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  • 2
    Electronic Resource
    Electronic Resource
    Weighted Dirichlet-type inequalities for Steiner symmetrization (1999)
    Springer
    Calculus of variations and partial differential equations 8 (1999), S. 15-25 
    Details
    ISSN: 1432-0835
    Keywords: Mathematics Subject Classification (1991):26D10, 51M16, 35J20, 35B99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. In this paper weighted Dirichlet-type inequalities for Steiner symmetrization are proved. Similar inequalities were known for the so-called starshaped rearrangements. Furthermore it is shown that the Steiner symmetrization is a mapping from $W^{1,1} _+ ({\Bbb R}^n)$ into itself.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s005260050114
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    Paper (German National Licenses)
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  • 3
    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: Mathematics Subject Classification:49K20, 49N60, 35R35, 35B65, 35M10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Let $\Omega$ be a ball in ${\Bbb R}^N$ , centered at zero, and let $u$ be a minimizer of the nonconvex functional $$R(v)=\int_{\Omega} {1\over 1+\vert \nabla v(x)\vert^2}dx$$ over one of the classes $C_M:= \{ w\in W_{loc}^{1,\infty}(\Omega)\mid 0\leq w(x)\leq M$ in $\Omega$ , $w$ concave $\}$ or $E_M:= \{ w\in W_{loc}^{1,2}(\Omega)\mid 0\leq w(x)\leq M$ in $\Omega$ , $\Delta w\leq 0$ in ${\cal D}'(\Omega)\}$ of admissible functions. Then $u$ 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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