On the Newton partially flat minimal resistance body type problems



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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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Official URL: http://www.ann.jussieu.fr/~comte/pdf/ComteDiaz8.pdf


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
Deposited On:01 Jun 2012 10:50
Last Modified:12 Dec 2018 15:07

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