Geodesic
Contact of a free boundary with a fixed boundary
Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 307-315 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_2000_191_2_a6,
     author = {N. N. Ural'tseva},
     title = {Contact of a~free boundary with a~fixed boundary},
     journal = {Sbornik. Mathematics},
     pages = {307--315},
     year = {2000},
     volume = {191},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_2_a6/}
}
TY  - JOUR
AU  - N. N. Ural'tseva
TI  - Contact of a free boundary with a fixed boundary
JO  - Sbornik. Mathematics
PY  - 2000
SP  - 307
EP  - 315
VL  - 191
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2000_191_2_a6/
LA  - en
ID  - SM_2000_191_2_a6
ER  - 
%0 Journal Article
%A N. N. Ural'tseva
%T Contact of a free boundary with a fixed boundary
%J Sbornik. Mathematics
%D 2000
%P 307-315
%V 191
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2000_191_2_a6/
%G en
%F SM_2000_191_2_a6
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/

[1] Caffarelli L. A., “The regularity of free boundaries in higher dimensions”, Acta Math., 139 (1977), 155–184 | DOI | MR

[2] Caffarelli L. A., “Compactness methods in free boundary problems”, Comm. Partial Differential Equations, 5:4 (1980), 427–448 | DOI | MR | Zbl

[3] Caffarelli L. A., Karp L., Shahgholian H., “Regularity of a free boundary with application to the Pompeiu problem”, TRITA-MAT-98-MA-36, ISSN, 1401–2278

[4] Apushkinskaya D. E., Uraltseva N. N., “O povedenii svobodnoi granitsy vblizi granitsy oblasti”, Zapiski nauch. sem. POMI, 221, POMI, SPb., 1995, 5–19 | MR

[5] Uraltseva N. N., “$C^1$ regulyarnost granitsy nekointsidentnogo mnozhestva v zadache s prepyatstviem”, Algebra i analiz, 8:2 (1996), 205–221 | MR | Zbl

[6] Uraltseva N. N., “O svoistvakh svobodnoi granitsy v okrestnosti tochek kontakta s izvestnoi granitsei”, Zapiski nauch. sem. POMI, 249, POMI, SPb., 1997, 303–312 | MR | Zbl