Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 5-19
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D. E. Apushkinskaya; N. N. Uraltseva. On the behavior of free boundaries near the boundary of the domain. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 5-19. http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a0/
@article{ZNSL_1995_221_a0,
author = {D. E. Apushkinskaya and N. N. Uraltseva},
title = {On the behavior of free boundaries near the boundary of the domain},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {5--19},
year = {1995},
volume = {221},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a0/}
}
TY - JOUR
AU - D. E. Apushkinskaya
AU - N. N. Uraltseva
TI - On the behavior of free boundaries near the boundary of the domain
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1995
SP - 5
EP - 19
VL - 221
UR - http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a0/
LA - ru
ID - ZNSL_1995_221_a0
ER -
%0 Journal Article
%A D. E. Apushkinskaya
%A N. N. Uraltseva
%T On the behavior of free boundaries near the boundary of the domain
%J Zapiski Nauchnykh Seminarov POMI
%D 1995
%P 5-19
%V 221
%U http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a0/
%G ru
%F ZNSL_1995_221_a0
Let $u$ be a solution of the obstacle problem $u\ge0$, $-\Delta u+f\ge0$, $u(-\Delta u+f)=0$ in a domain $\Omega\subset\mathbb R^n$. In this paper, the behaviour of the free boundary in a neighborhood of $\partial\Omega$ is studied. It is proved that under some conditions the free boundary touches $\partial\Omega$ at contact points. Bibliography: 4 titles.
