# On the Newton partially flat minimal resistance body type problems

M. Comte; Jesus Ildefonso Díaz

Journal of the European Mathematical Society (2005)

- Volume: 007, Issue: 4, page 395-411
- ISSN: 1435-9855

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topComte, 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 -

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