Geodesic
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

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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. 
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     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},
     publisher = {mathdoc},
     volume = {221},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a0/}
}
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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/