Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 89-92
Citer cet article
L. G. Makar-Limanov. Solution of Dirichlet's problem for the equation $\Delta u=-1$ in a convex region. Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 89-92. http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a12/
@article{MZM_1971_9_1_a12,
author = {L. G. Makar-Limanov},
title = {Solution of {Dirichlet's} problem for the equation $\Delta u=-1$ in a convex region},
journal = {Matemati\v{c}eskie zametki},
pages = {89--92},
year = {1971},
volume = {9},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a12/}
}
TY - JOUR
AU - L. G. Makar-Limanov
TI - Solution of Dirichlet's problem for the equation $\Delta u=-1$ in a convex region
JO - Matematičeskie zametki
PY - 1971
SP - 89
EP - 92
VL - 9
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a12/
LA - ru
ID - MZM_1971_9_1_a12
ER -
%0 Journal Article
%A L. G. Makar-Limanov
%T Solution of Dirichlet's problem for the equation $\Delta u=-1$ in a convex region
%J Matematičeskie zametki
%D 1971
%P 89-92
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a12/
%G ru
%F MZM_1971_9_1_a12
Let $u$ be a solution of the following boundary-value problem: $u|_\Gamma=0$, where $\Gamma$ is a closed convex curve and $\Delta u=-1$ in the region $D$ bounded by $\Gamma$. Then $u$ has only one local maximum, and all its level curves are convex.
