@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://archive.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://archive.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://archive.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, Serie 6, Volume 13 (2004) no. 2, pp. 289-311. http://archive.numdam.org/item/AFST_2004_6_13_2_289_0/
[1] A free boundary problem for semilinear elliptic equations, J. Reine Angew. Math. 368, p. 63-107 (1986). | MR | Zbl
, -[2] A Semi-elliptic System Arising in the Theory of type-II Superconductivity, Comm. Appl. Nonlinear Anal. 1, p. 1-21 (1994). | Zbl
, , -[3] On the method of moving planes and the sliding method, Bol. Soc. Braseleira Mat. (N.S.)22, 1-37 (1991). | MR | Zbl
, -[4] 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] 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] The Smoothness of Solutions to Nonlinear Variational Inequalities, Indiana Univ. Math. J. 23 (9), p. 831-844 (1974). | MR | Zbl
, -[7] Fully Nonlinear Elliptic Equations, Colloquium Publications. Amer. Math. Soc. 43 (1995). | MR | Zbl
, -[8] Compactness Methods in Free Boundary Problems, Comm. Partial Differential Equations 5 (4), p. 427-448 (1980). | MR | Zbl
-[9] 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] Free boundary problem in higher dimensions , Acta Math. 139, p. 155-184 (1977). | Zbl
-[11] The Obstacle Problem revisited, J. Fourier Anal. Appl. 4, p. 383-402 (1998). | MR | Zbl
-[12] Free Boundary Regularity for a Problem Arising in Superconductivity, Arch. Ration. Mech. Anal. 171 (1), p. 115-128 (2004). | MR | Zbl
, , -[13] A Mean-field Model of Superconducting vortices, European J. Appl. Math. 7, p. 97-111 (1996). | MR | Zbl
, , -[14] Variational Principles and Free Boundary Problems, Pure and applied mathematics, ISSN 0079-8185, a Wiley-Interscience publication, (1982). | MR | Zbl
-[15] Elliptic Partial Differential Equations of Second Order, Springer-Verlag (1997 ).
, -[16] Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci 4, p. 373-391 (1977). | Numdam | MR | Zbl
, -[17] An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, (1980). | MR | Zbl
, -[18] Linear and Quasilinear Elliptic Equations, New York: Academic Press, (1968). | MR | Zbl
, -[19] An unpublished course at Courant Institute of Mathematical Sciences, (1990).
-[20] 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] Multiple Integrals in the Caculus of Variations , Springer-Verlag, Berlin- Heidelberg -New York, (1966). | MR | Zbl
-[22] Obstacle Problems in Mathematical Physics , North-Holland, (1987). | MR | Zbl
-[23] 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] 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] Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation, Archive for Rational Mechanics and Analysis 149, p. 329-365 (1999). | MR | Zbl
-[26] A homogeneity improvement approach to the obstacle problem, Invent. math. 138, p. 23-50 (1999). | MR | Zbl
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