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. 
@article{AIHPC_2009__26_4_1149_0,
     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},
     mrnumber = {2542718},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.07.003/}
}
TY  - JOUR
AU  - BriançOn, Tanguy
AU  - Lamboley, Jimmy
TI  - Regularity of the Optimal Shape for the First Eigenvalue of the Laplacian With Volume and Inclusion Constraints
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
DA  - 2009///
SP  - 1149
EP  - 1163
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2008.07.003/
UR  - https://www.ams.org/mathscinet-getitem?mr=2542718
UR  - https://doi.org/10.1016/j.anihpc.2008.07.003
DO  - 10.1016/j.anihpc.2008.07.003
LA  - en
ID  - AIHPC_2009__26_4_1149_0
ER  - 
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 618549 | Zbl 0449.35105

[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 732100 | Zbl 0844.35137

[3] Briançon T., Regularity of Optimal Shapes for the Dirichlet's Energy With Volume Constraint, ESAIM: COCV 10 (2004) 99-122. | Numdam | MR 2084257 | Zbl 1118.35078

[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 2133659 | Zbl 1062.49035

[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 1217590 | Zbl 0811.49028

[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 2082392

[7] Crouzeix M., Variational Approach of a Magnetic Shaping Problem, Eur. J. Mech. B/Fluids 10 (1991) 527-536. | MR 1139607 | Zbl 0741.76089

[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 1158660 | Zbl 0804.28001

[10] Giusti E., Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel-Boston, MA, 1984. | MR 775682 | Zbl 0545.49018

[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 1390686 | Zbl 0846.31005

[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 1760437 | Zbl 0960.49028

[13] Wagner A., Optimal Shape Problems for Eigenvalues, Comm. Partial Differential Equations 30 (7-9) (2005). | MR 2180294 | Zbl 1121.35038

[14] Weiss G. S., Partial Regularity for Weak Solutions of an Elliptic Free Boundary Problem, Comm. Partial Differential Equations 23 (1998) 439-457. | MR 1620644 | Zbl 0897.35017

[15] Weiss G. S., Partial Regularity for a Minimum Problem With Free Boundary, J. Geom. Anal. 9 (2) (1999) 317-326. | MR 1759450 | Zbl 0960.49026

Cité par Sources :