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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

PDF
Restringido a Repository staff only 166kB |

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

## Abstract

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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