Shape optimization and trial methods for free boundary problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 7, pp. 805-825. 
@article{M2AN_1997__31_7_805_0,
     author = {Tiihonen, Timo},
     title = {Shape optimization and trial methods for free boundary problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {805--825},
     publisher = {Elsevier},
     volume = {31},
     number = {7},
     year = {1997},
     mrnumber = {1489173},
     zbl = {0891.65131},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1997__31_7_805_0/}
}
TY  - JOUR
AU  - Tiihonen, Timo
TI  - Shape optimization and trial methods for free boundary problems
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1997
SP  - 805
EP  - 825
VL  - 31
IS  - 7
PB  - Elsevier
UR  - http://archive.numdam.org/item/M2AN_1997__31_7_805_0/
LA  - en
ID  - M2AN_1997__31_7_805_0
ER  - 
%0 Journal Article
%A Tiihonen, Timo
%T Shape optimization and trial methods for free boundary problems
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1997
%P 805-825
%V 31
%N 7
%I Elsevier
%U http://archive.numdam.org/item/M2AN_1997__31_7_805_0/
%G en
%F M2AN_1997__31_7_805_0
Tiihonen, Timo. Shape optimization and trial methods for free boundary problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 7, pp. 805-825. http://archive.numdam.org/item/M2AN_1997__31_7_805_0/

[1] H. W. Alt, L. A. Cafarelli, 1981, Existence and regularity for a minimum problem with free boundary, J. Reine angew. Math. 325, 105-144. | MR | Zbl

[2] C. Cuvelier, R. M. S. M. Schulkes, 1990, Some numerical methods for the computation of capillary free boundaries governed by the Navier-Stokes equations, Siam Review 32, 355-423. | MR | Zbl

[3] M. C. Delfour, 1990, Shape Derivatives and Differentiability of Min Max, in « Shape Optimization and Free Boundaries, M. C. Delfour and G. Sabidussi (eds.) », Kluwer, Dordrecht, pp. 35-111. | MR | Zbl

[4] M. C. Delfour, J. P. Zolésio, 1991, Anatomy of the shape Hessian, Ann. Mat. Pura Appl. (4) 158, 315-339. | MR | Zbl

[5] M. C. Delfour, J. P. Zolésio, 1991, Velocity method and Lagrangian formulation for the computation of the shape Hessian, SIAM J. Contrat Optim. 29, 1414-1442. | MR | Zbl

[6] M. Flucher, M. Rumpf, 1997, Bernoulli's free-boundary problem, qualitative theory and numerical approximation, J. Reine angew. Math. 86. | MR | Zbl

[7] P. R. Garabedian, 1956, The mathematical theory of three dimensional cavities and jets, Bull. Amer. Math. Soc, 62, 219-235. | MR | Zbl

[8] J. Haslinger, R. Neittaanmäki, 1996, « Finite element approximation for optimal shape, material and topology design », John Wiley. | MR | Zbl

[9] O. Pironneau, 1984, « Optimal shape design for elliptic Systems », Springer Verlag. | MR | Zbl

[10] J. Sokolowski, J. R. Zolésio, 1992, « Introduction to Shape Optimization», Springer Verlag. | MR | Zbl

[11] T. Tiihonen, J. Järvinen, 1992, On fixed point (trial) methods for free boundary problems, in « Free boundary problems in continuum mechanics », S. N. Antontsev, K.-H. Hoffmann, A. M. Khludnev (eds.), ISNM 106, Birkhauser Verlag, Basel, pp. 339-350. | MR | Zbl

[12] J. P. Zolésio, 1979, « Identification de domaines par déformations», Thèse d'état, Univ. Nice.

[13] J. P. Zolésio, 1990, Introduction to shape optimization problems and free boundary problems, in « Shape Optimization and Free Boundaries », M. C. Delfour and G. Sabidussi (eds.), Kluwer, Dordrecht, pp. 397-457. | MR | Zbl

[14] J. P. Zolésio, 1994, Weak Shape Formulation of Free Boundary Problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci., XXI, 1, 397-457. | Numdam | MR | Zbl