%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Comte, M.
%T On the Newton partially flat minimal resistance body type problems
%D 2005
%@ 1435-9855
%U https://hdl.handle.net/20.500.14352/49974
%X 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.
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