@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 SP - 1149 EP - 1163 VL - 26 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/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 -
%0 Journal Article %A BriançOn, Tanguy %A Lamboley, Jimmy %T Regularity of the Optimal Shape for the First Eigenvalue of the Laplacian With Volume and Inclusion Constraints %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 1149-1163 %V 26 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2008.07.003/ %R 10.1016/j.anihpc.2008.07.003 %G en %F 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, Volume 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] Existence and Regularity for a Minimum Problem With Free Boundary, J. Reine Angew. Math. 325 (1981) 105-144. | MR | Zbl
, ,[2] Variational Problems With Two Phases and Their Free Boundaries, Trans. Amer. Math. Soc. 282 (2) (1984) 431-461. | MR | Zbl
, , ,[3] Regularity of Optimal Shapes for the Dirichlet's Energy With Volume Constraint, ESAIM: COCV 10 (2004) 99-122. | Numdam | MR | Zbl
,[4] Lipschitz Continuity of State Functions in Some Optimal Shaping, Calc. Var. Partial Differential Equations 23 (1) (2005) 13-32. | MR | Zbl
, , ,[5] An Existence Result for a Class of Shape Optimization Problems, Arch. Ration. Mech. Anal. 122 (1993) 183-195. | MR | Zbl
, ,[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
, , ,[7] 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] Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. | MR | Zbl
, ,[10] Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel-Boston, MA, 1984. | MR | Zbl
,[11] 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] 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] Optimal Shape Problems for Eigenvalues, Comm. Partial Differential Equations 30 (7-9) (2005). | MR | Zbl
,[14] Partial Regularity for Weak Solutions of an Elliptic Free Boundary Problem, Comm. Partial Differential Equations 23 (1998) 439-457. | MR | Zbl
,[15] Partial Regularity for a Minimum Problem With Free Boundary, J. Geom. Anal. 9 (2) (1999) 317-326. | MR | Zbl
,Cited by Sources: