On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling

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1. [1] Alt ( H.W.) , Phillips ( D.). - A free boundary problem for semilinear elliptic equations, J. Reine Angew. Math.368, p. 63-107 (1986). Zbl0598.35132MR850615
2. [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). Zbl0866.35030
3. [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). Zbl0784.35025MR1159383
4. [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 ). Zbl0970.35031MR1766555
5. [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 Boundaries2, p. 181-200 (2000). Zbl0989.35146MR1760411
6. [6] Brézis ( H. ), Kinderlehrer ( D.). - The Smoothness of Solutions to Nonlinear Variational Inequalities, Indiana Univ. Math. J.23 (9), p. 831-844 (1974). Zbl0278.49011MR361436
7. [7] Cabré ( X.) , Caffarelli ( L.A.). - Fully Nonlinear Elliptic Equations, Colloquium Publications. Amer. Math. Soc.43 (1995). Zbl0834.35002MR1351007
8. [8] Caffarelli ( L.A.). - Compactness Methods in Free Boundary Problems, Comm. Partial Differential Equations5 (4), p. 427-448 (1980). Zbl0437.35070MR567780
9. [9] Caffarelli ( L.A.). - A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets, Boll. Un. Mat. Ital.A18 (5), p. 109-113 (1981). Zbl0453.35085MR607212
10. [10] Caffarelli ( L.A.). - Free boundary problem in higher dimensions , Acta Math.139, p. 155-184 (1977). Zbl0386.35046
11. [11] Caffarelli ( L.A.). - The Obstacle Problem revisited, J. Fourier Anal. Appl.4, p. 383-402 (1998). Zbl0928.49030MR1658612
12. [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). Zbl1072.35203MR2029533
13. [13] Chapman ( S.J.), Rubinstein ( J.), Schatzman ( M.). — A Mean-field Model of Superconducting vortices, European J. Appl. Math.7, p. 97-111 (1996). Zbl0849.35135MR1388106
14. [14] Friedman ( A.). - Variational Principles and Free Boundary Problems, Pure and applied mathematics, ISSN 0079-8185, a Wiley-Interscience publication, (1982). Zbl0564.49002MR679313
15. [15] Gilbarg ( D. ) , Trudinger ( N.S.). - Elliptic Partial Differential Equations of Second Order, Springer-Verlag (1997 ). 
16. [16] Kinderlehrer ( D.), Nirenberg ( L.). - Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci4, p. 373-391 (1977). Zbl0352.35023MR440187
17. [17] D. Kinderlehrer , G. Stampacchia. - An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, (1980). Zbl0457.35001MR567696
18. [18] Ladyshenskaya ( O.A.), Ural'tseva ( N.N.). - Linear and Quasilinear Elliptic Equations, New York: Academic Press, (1968). Zbl0164.13002MR244627
19. [19] Lin ( F.H.). - An unpublished course at CourantInstitute of Mathematical Sciences, (1990). 
20. [20] Monneau ( R.). - On the Number of Singularities for the Obstacle Problem in Two Dimensions, J. of Geometric Analysis13 (2), p. 359-389 (2003). Zbl1041.35093MR1967031
21. [21] Morrey ( C.B. ). - Multiple Integrals in the Caculus of Variations , Springer-Verlag, Berlin- Heidelberg -New York, (1966). Zbl0142.38701MR202511
22. [22] J.F. Rodrigues . - Obstacle Problems in Mathematical Physics , North-Holland, (1987). Zbl0606.73017MR880369
23. [23] Sandier ( E.), Serfaty ( S.). - A Rigorous Derivation of a Free-Boundary Problem Arising in Superconductivity, Annales Scientifiques de l'ENS33, p. 561-592, (2000 ). Zbl1174.35552MR1832824
24. [24] Sandier ( E.), Serfaty ( S.). - On the Energy of Type-II Superconductors in the Mixed Phase, Reviews in Mathematical Physics12, No 9, p. 1219-1257, (2000 ). Zbl0964.49006MR1794239
25. [25] Serfaty ( S.). - Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation, Archive for Rational Mechanics and Analysis149, p. 329-365 (1999). Zbl0959.35154MR1731999
26. [26] Weiss ( G.S. ). - A homogeneity improvement approach to the obstacle problem, Invent. math.138, p. 23-50 (1999). Zbl0940.35102MR1714335