@article{AIHPC_2009__26_4_1149_0, author = {Brian\c cOn, 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}, volume = {26}, year = {2009}, pages = {1149-1163}, doi = {10.1016/j.anihpc.2008.07.003}, mrnumber = {2542718}, zbl = {pre05590477}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_4_1149_0} }
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) pp. 1149-1163. doi : 10.1016/j.anihpc.2008.07.003. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_4_1149_0/
[1] Existence and Regularity for a Minimum Problem With Free Boundary, J. Reine Angew. Math. 325 (1981) 105-144. | MR 618549 | Zbl 0449.35105
, ,[2] Variational Problems With Two Phases and Their Free Boundaries, Trans. Amer. Math. Soc. 282 (2) (1984) 431-461. | MR 732100 | Zbl 0844.35137
, , ,[3] 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] 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] An Existence Result for a Class of Shape Optimization Problems, Arch. Ration. Mech. Anal. 122 (1993) 183-195. | MR 1217590 | Zbl 0811.49028
, ,[6] 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 | Zbl pre02166797
, , ,[7] 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. | Zbl pre05633735
[9] Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. | MR 1158660 | Zbl 0804.28001
, ,[10] Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel-Boston, MA, 1984. | MR 775682 | Zbl 0545.49018
,[11] 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] 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] Optimal Shape Problems for Eigenvalues, Comm. Partial Differential Equations 30 (7-9) (2005). | MR 2180294 | Zbl 1121.35038
,[14] 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] Partial Regularity for a Minimum Problem With Free Boundary, J. Geom. Anal. 9 (2) (1999) 317-326. | MR 1759450 | Zbl 0960.49026
,