Díaz Díaz, Jesús IldefonsoComte, M.2023-06-202023-06-2020051435-985510.4171/JEMS/33https://hdl.handle.net/20.500.14352/49974We 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.engjournal articlehttp://www.ann.jussieu.fr/~comte/pdf/ComteDiaz8.pdfhttp://www.ems.org/restricted access517.95517.98Newton problemobstacle problemquasilinear elliptic operatorsflat solutionsGeometría diferencialAnálisis funcional y teoría de operadores1204.04 Geometría Diferencial