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On the Newton partially flat minimal resistance body type problems



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Díaz Díaz, Jesús Ildefonso y 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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URL Oficial: http://www.ann.jussieu.fr/~comte/pdf/ComteDiaz8.pdf

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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.

Tipo de documento:Artículo
Palabras clave:Newton problem; obstacle problem; quasilinear elliptic operators; flat solutions
Materias:Ciencias > Matemáticas > Geometría diferencial
Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:15456
Depositado:01 Jun 2012 10:50
Última Modificación:12 Dic 2018 15:07

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