On the Newton partially flat minimal resistance body type problems

Comte, M., and Díaz, Jesus Ildefonso. "On the Newton partially flat minimal resistance body type problems." Journal of the European Mathematical Society 007.4 (2005): 395-411. <http://eudml.org/doc/277690>.

@article{Comte2005,
abstract = {We study the flat region of stationary points of the functional $\int _\Omega F(|\nabla u(x)|)dx$ under the constraint $u\le M$, where $\Omega $ is a bounded domain in $\mathbb \{R\}^2$. 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.},
author = {Comte, M., Díaz, Jesus Ildefonso},
journal = {Journal of the European Mathematical Society},
keywords = {stationary points; minimal resistance body problems; Newton problem; obstacle problem; flat solutions; quasilinear elliptic operators; quasilinear elliptic operators; Newton problem; obstacle problem; aerodynamical minimal resistance},
language = {eng},
number = {4},
pages = {395-411},
publisher = {European Mathematical Society Publishing House},
title = {On the Newton partially flat minimal resistance body type problems},
url = {http://eudml.org/doc/277690},
volume = {007},
year = {2005},
}

TY - JOUR
AU - Comte, M.
AU - Díaz, Jesus Ildefonso
TI - On the Newton partially flat minimal resistance body type problems
JO - Journal of the European Mathematical Society
PY - 2005
PB - European Mathematical Society Publishing House
VL - 007
IS - 4
SP - 395
EP - 411
AB - We study the flat region of stationary points of the functional $\int _\Omega F(|\nabla u(x)|)dx$ under the constraint $u\le M$, where $\Omega $ is a bounded domain in $\mathbb {R}^2$. 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.
LA - eng
KW - stationary points; minimal resistance body problems; Newton problem; obstacle problem; flat solutions; quasilinear elliptic operators; quasilinear elliptic operators; Newton problem; obstacle problem; aerodynamical minimal resistance
UR - http://eudml.org/doc/277690
ER -