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On the Newton partially flat minimal resistance body type problems

Díaz Díaz, Jesús Ildefonso and Comte, M. (2005) On the Newton partially flat minimal resistance body type problems. Journal of the European Mathematical Society, 7 (4). pp. 395-411. ISSN 1435-9855

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Abstract

We study the flat region of stationary points of the functional integral(Omega) F(|del u(x)|) dx under the constraint u <= M, where Omega is a bounded domain in R-2. Here F( s) is a function which is concave for s small and convex for s large, and M > 0 is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when Omega is a ball. We also analyze some other qualitative properties. Moreover, we show the uniqueness of a radial solution minimizing the above mentioned functional. Finally, we consider nonsymmetric domains Omega and provide sufficient conditions which ensure that a stationary solution has a flat part.


Item Type:Article
Uncontrolled Keywords:Newton problem; obstacle problem; quasilinear elliptic operators; flat solutions
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15456
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