Geodesic
On the Newton partially flat minimal resistance body type problems
Journal of the European Mathematical Society, Tome 7 (2005) no. 4, pp. 395-411

Voir la notice de l'article provenant de la source EMS Press

We study the flat region of stationary points of the functional ∫Ω​F(∣∇u(x)∣)dx under the constraint u≤M, where Ω is a bounded domain of R2. 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 Ω is a ball. We analyze also some other qualitative properties. Moreover, we show the uniqueness of a radial solution minimizing the above mentioned functional. Finally, we consider nonsymmetric domains Ω and provide sufficient conditions which insure that a stationary solution has a flat part.
DOI : 10.4171/jems/33
Classification : 49-XX, 35-XX, 00-XX
Keywords: stationary points, minimal resistance body problems, Newton problem 
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     title = {On the {Newton} partially flat minimal resistance body type problems},
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     pages = {395--411},
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Myriam Comte; Jesús Ildefonso Díaz. On the Newton partially flat minimal resistance body type problems. Journal of the European Mathematical Society, Tome 7 (2005) no. 4, pp. 395-411. doi: 10.4171/jems/33

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