Geodesic
Contact of a~free boundary with a~fixed boundary
Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 307-315

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For a simple elliptic obstacle problem the behaviour of the free boundary is studied near its points of contact with the fixed boundary of the domain. An earlier result of the author on the $C^1$-regularity of the boundary $\partial\mathscr N$ of the non-coincidence set is refined. It is shown that the previously imposed Lipschitz condition on $\partial\mathscr N$ can be dispensed with. 
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     author = {N. N. Ural'tseva},
     title = {Contact of a~free boundary with a~fixed boundary},
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     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_2_a6/}
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N. N. Ural'tseva. Contact of a~free boundary with a~fixed boundary. Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 307-315. http://geodesic.mathdoc.fr/item/SM_2000_191_2_a6/