On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 13 (2004) no. 2, pp. 289-311. 
@article{AFST_2004_6_13_2_289_0,
     author = {Monneau, R\'egis},
     title = {On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {289--311},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 13},
     number = {2},
     year = {2004},
     mrnumber = {2126745},
     zbl = {1081.35162},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2004_6_13_2_289_0/}
}
TY  - JOUR
AU  - Monneau, Régis
TI  - On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2004
SP  - 289
EP  - 311
VL  - 13
IS  - 2
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2004_6_13_2_289_0/
LA  - en
ID  - AFST_2004_6_13_2_289_0
ER  - 
%0 Journal Article
%A Monneau, Régis
%T On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2004
%P 289-311
%V 13
%N 2
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/item/AFST_2004_6_13_2_289_0/
%G en
%F AFST_2004_6_13_2_289_0
Monneau, Régis. On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 13 (2004) no. 2, pp. 289-311. http://www.numdam.org/item/AFST_2004_6_13_2_289_0/

[1] Alt (H.W.) , Phillips ( D.). - A free boundary problem for semilinear elliptic equations, J. Reine Angew. Math. 368, p. 63-107 (1986). | MR | Zbl

[2] Berestycki ( H.), Bonnet (A.), Chapman (S.J.). - A Semi-elliptic System Arising in the Theory of type-II Superconductivity, Comm. Appl. Nonlinear Anal. 1, p. 1-21 (1994). | Zbl

[3] Berestycki ( H.), Nirenberg (L.). - On the method of moving planes and the sliding method, Bol. Soc. Braseleira Mat. (N.S.)22, 1-37 (1991). | MR | Zbl

[4] Bonnet (A. ), Chapman (S.J.), Monneau (R.). - Convergence of Meissner minimisers of the Ginzburg-Landau energy of superconductivity as kappa tends to infinity, SIAM J. Math. Anal. 31 (6), p. 1374-1395 (2000 ). | MR | Zbl

[5] Bonnet (A. ), Monneau (R.). - Distribution of vortices in a type II superconductor as a free boundary problem: Existence and regularity via Nash-Moser theory, Interfaces and Free Boundaries 2, p. 181-200 (2000). | MR | Zbl

[6] Brézis (H. ), Kinderlehrer (D.). - The Smoothness of Solutions to Nonlinear Variational Inequalities, Indiana Univ. Math. J. 23 (9), p. 831-844 (1974). | MR | Zbl

[7] Cabré (X.) , Caffarelli ( L.A.). - Fully Nonlinear Elliptic Equations, Colloquium Publications. Amer. Math. Soc. 43 (1995). | MR | Zbl

[8] Caffarelli ( L.A.). - Compactness Methods in Free Boundary Problems, Comm. Partial Differential Equations 5 (4), p. 427-448 (1980). | MR | Zbl

[9] Caffarelli ( L.A.). - A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets, Boll. Un. Mat. Ital. A 18 (5), p. 109-113 (1981). | MR | Zbl

[10] Caffarelli ( L.A.). - Free boundary problem in higher dimensions , Acta Math. 139, p. 155-184 (1977). | Zbl

[11] Caffarelli ( L.A.). - The Obstacle Problem revisited, J. Fourier Anal. Appl. 4, p. 383-402 (1998). | MR | Zbl

[12] Caffarelli ( L.A.), Salazar (J.), Shahgholian (H.). - Free Boundary Regularity for a Problem Arising in Superconductivity, Arch. Ration. Mech. Anal. 171 (1), p. 115-128 (2004). | MR | Zbl

[13] Chapman ( S.J.), Rubinstein (J.), Schatzman (M.). - A Mean-field Model of Superconducting vortices, European J. Appl. Math. 7, p. 97-111 (1996). | MR | Zbl

[14] Friedman ( A.). - Variational Principles and Free Boundary Problems, Pure and applied mathematics, ISSN 0079-8185, a Wiley-Interscience publication, (1982). | MR | Zbl

[15] Gilbarg (D. ) , Trudinger ( N.S.). - Elliptic Partial Differential Equations of Second Order, Springer-Verlag (1997 ).

[16] Kinderlehrer ( D.), Nirenberg (L.). - Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci 4, p. 373-391 (1977). | Numdam | MR | Zbl

[17] D. Kinderlehrer , G. Stampacchia. - An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, (1980). | MR | Zbl

[18] Ladyshenskaya ( O.A.), Ural'Tseva (N.N.). - Linear and Quasilinear Elliptic Equations, New York: Academic Press, (1968). | MR | Zbl

[19] Lin (F.H.). - An unpublished course at Courant Institute of Mathematical Sciences, (1990).

[20] Monneau ( R.). - On the Number of Singularities for the Obstacle Problem in Two Dimensions, J. of Geometric Analysis 13 (2), p. 359-389 (2003). | MR | Zbl

[21] Morrey (C.B. ). - Multiple Integrals in the Caculus of Variations , Springer-Verlag, Berlin- Heidelberg -New York, (1966). | MR | Zbl

[22] J.F. Rodrigues . - Obstacle Problems in Mathematical Physics , North-Holland, (1987). | MR | Zbl

[23] Sandier ( E.), Serfaty (S.). - A Rigorous Derivation of a Free-Boundary Problem Arising in Superconductivity, Annales Scientifiques de l'ENS 33, p. 561-592, (2000 ). | Numdam | MR | Zbl

[24] Sandier ( E.), Serfaty (S.). - On the Energy of Type-II Superconductors in the Mixed Phase, Reviews in Mathematical Physics 12, No 9, p. 1219-1257, (2000 ). | MR | Zbl

[25] Serfaty ( S.). - Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation, Archive for Rational Mechanics and Analysis 149, p. 329-365 (1999). | MR | Zbl

[26] Weiss (G.S. ). - A homogeneity improvement approach to the obstacle problem, Invent. math. 138, p. 23-50 (1999). | MR | Zbl