no. 4
Regularity of the Optimal Shape for the First Eigenvalue of the Laplacian With Volume and Inclusion Constraints
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1149-1163. 
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     author = {Brian\c{c}On, Tanguy and Lamboley, Jimmy},
     title = {Regularity of the {Optimal} {Shape} for the {First} {Eigenvalue} of the {Laplacian} {With} {Volume} and {Inclusion} {Constraints}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1149--1163},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.07.003},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.07.003/}
}
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BriançOn, Tanguy; Lamboley, Jimmy. Regularity of the Optimal Shape for the First Eigenvalue of the Laplacian With Volume and Inclusion Constraints. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1149-1163. doi : 10.1016/j.anihpc.2008.07.003. http://www.numdam.org/articles/10.1016/j.anihpc.2008.07.003/

[1] Alt H. W., Caffarelli L. A., Existence and Regularity for a Minimum Problem With Free Boundary, J. Reine Angew. Math. 325 (1981) 105-144. | MR | Zbl

[2] Alt H. W., Caffarelli L. A., Friedman A., Variational Problems With Two Phases and Their Free Boundaries, Trans. Amer. Math. Soc. 282 (2) (1984) 431-461. | MR | Zbl

[3] Briançon T., Regularity of Optimal Shapes for the Dirichlet's Energy With Volume Constraint, ESAIM: COCV 10 (2004) 99-122. | Numdam | MR | Zbl

[4] Briançon T., Hayouni M., Pierre M., Lipschitz Continuity of State Functions in Some Optimal Shaping, Calc. Var. Partial Differential Equations 23 (1) (2005) 13-32. | MR | Zbl

[5] Buttazzo G., Dal Maso G., An Existence Result for a Class of Shape Optimization Problems, Arch. Ration. Mech. Anal. 122 (1993) 183-195. | MR | Zbl

[6] Caffarelli L. A., Jerison D., Kenig C. E., Global Energy Minimizers for Free Boundary Problems and Full Regularity in Three Dimensions, in: Contemp. Math., vol. 350, Amer. Math. Soc., Providence, RI, 2004, pp. 83-97. | MR

[7] Crouzeix M., Variational Approach of a Magnetic Shaping Problem, Eur. J. Mech. B/Fluids 10 (1991) 527-536. | MR | Zbl

[8] D. De Silva, D. Jerison, A singular energy minimizing free boundary, J. Reine Angew. Math., in press.

[9] Evans L. C., Gariepy R. F., Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. | MR | Zbl

[10] Giusti E., Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel-Boston, MA, 1984. | MR | Zbl

[11] Gustafsson B., Shahgholian H., Existence and Geometric Properties of Solutions of a Free Boundary Problem in Potential Theory, J. Reine Angew. Math. 473 (1996) 137-179. | MR | Zbl

[12] Hayouni M., Sur La Minimisation De La Première Valeur Propre Du Laplacien, C. R. Acad. Sci. Paris, Sér. I 330 (7) (2000) 551-556. | MR | Zbl

[13] Wagner A., Optimal Shape Problems for Eigenvalues, Comm. Partial Differential Equations 30 (7-9) (2005). | MR | Zbl

[14] Weiss G. S., Partial Regularity for Weak Solutions of an Elliptic Free Boundary Problem, Comm. Partial Differential Equations 23 (1998) 439-457. | MR | Zbl

[15] Weiss G. S., Partial Regularity for a Minimum Problem With Free Boundary, J. Geom. Anal. 9 (2) (1999) 317-326. | MR | Zbl

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