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
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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 |
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| Deposited On: | 01 Jun 2012 10:50 |
| Last Modified: | 06 Feb 2014 10:25 |
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