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
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