Geodesic
When does the free boundary enter into corner points of the fixed boundary?
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 213-225

Voir la notice de l'article provenant de la source Math-Net.Ru

Our prime goal in this note is to lay the ground for studying free boundaries close to the corner points of a fixed, Lipschitz boundary. Our study is restricted to 2-space dimensions, and to the obstacle problem. Our main result states that the free boundary can not enter into a corner $x^0$ of the fixed boundary, if the (interior) angle is less than $\pi$, provided the boundary datum is zero close to the point $x^0$. For larger angles and other boundary datum the free boundary may enter into corners, as discussed in the text. 
@article{ZNSL_2004_310_a10,
     author = {H. Shahgholian},
     title = {When does the free boundary enter into corner points of the fixed boundary?},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {213--225},
     publisher = {mathdoc},
     volume = {310},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a10/}
}
TY  - JOUR
AU  - H. Shahgholian
TI  - When does the free boundary enter into corner points of the fixed boundary?
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 213
EP  - 225
VL  - 310
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a10/
LA  - en
ID  - ZNSL_2004_310_a10
ER  - 
%0 Journal Article
%A H. Shahgholian
%T When does the free boundary enter into corner points of the fixed boundary?
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 213-225
%V 310
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a10/
%G en
%F ZNSL_2004_310_a10
H. Shahgholian. When does the free boundary enter into corner points of the fixed boundary?. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 213-225. http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a10/