@article{M2AN_2000__34_4_811_0, author = {Dambrine, Marc and Pierre, Michel}, title = {About stability of equilibrium shapes}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {34}, year = {2000}, pages = {811-834}, mrnumber = {1784487}, zbl = {0966.49023}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_2000__34_4_811_0} }
Dambrine, Marc; Pierre, Michel. About stability of equilibrium shapes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 811-834. http://gdmltest.u-ga.fr/item/M2AN_2000__34_4_811_0/
[1] Formage d'une lame métallique liquide. Calculs et expériences. J. Mec. Theor. Appl. 2 (1983) 977-989. | Zbl 0564.76119
, and ,[2] Anatomy of the Shape Hessian Via Lie Brackets. Ann. Mat. Pura Appl.(IV) CLXXIII (1997) 27-143. | MR 1625559 | Zbl 0939.49023
and ,[3] Variational approach of a magnetic shaping problem. Eur. J. Mech. B Fluids 10 (1991) 527-536. | MR 1139607 | Zbl 0741.76089
,[4] Hessiennes de formes et stabilité de formes critiques. Ph.D. thesis, Université de Rennes 1, France (2000).
,[5] Analyse mathématique et calcul numérique pour les sciences et les techniques, Tome 2. Masson, Paris (1985). | MR 902801 | Zbl 0749.35005
and ,[6] Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian. SIAM Control Optim. 29 (1991) 1414-1442. | MR 1132189 | Zbl 0747.49007
and ,[7] On the two dimensional magnetic shaping problem without surface tension. Report, Analysis and numerical analysis, 07.90, École Polytechnique Fédérale de Lausanne (1990).
,[8] Stability of the solutions of the bidimensional magnetic shaping problem in absence of surface tension. Eur. J. Mech. B Fluids 10 (1991) 513-526. | MR 1139606 | Zbl 0741.76025
,[9] A stabihty resuit for the magnetic shaping problem. Z. Angew. Math. Phys. 45 (1994) 543-555. | MR 1289660 | Zbl 0809.76037
,[10] Elliptic partial differential equations of second order. Springer-Verlag, Berlin, 2nd edn (1983). | MR 737190 | Zbl 0562.35001
and ,[11] Stability in shaping problems. (to appear).
and ,[12] About existence of a free boundary in electromagnetic shaping, in Recent advances in nonlinear elliptic and parabolic problems (Nancy, 1988), Longman Sci. Tech., Harlow (1989) 283-293. | MR 1035015 | Zbl 0696.35194
and ,[13] Un problème inverse en formage des métaux liquides. RAIRO. Modél. Math. Anal. Numér. 23 (1989) 155-177. | Numdam | MR 1015924 | Zbl 0672.65101
and ,[14] About critical points of the energy in the electromagnetic shaping problem, in Boundary Control and Boundary variations, Springer-Verlag, 178 (1991) 238-252. | MR 1173448 | Zbl 0820.35139
and ,[15] About existence of equilibria in electromagnetic casting. Quart. Appl. Math. 49 (1991) 563-575. | MR 1121687 | Zbl 0731.76092
and ,[16] Sur le contrôle par un domaine géométrique. Rapport du L.A. 189, Université Paris VI, France (1976).
and ,[17] Contribution en Optimisation de Formes et Applications. Ph.D. thesis, Université Henri Poincaré, Nancy (1996).
,[18] Structure of Shape Derivatives. Prépublication IRMAR, n° 00-07, Rennes (2000).
and ,[19] Note on a Hamiltonian formalism for the flow of a magnetic fluid with a free surface. J. Fluid Mech. 181 (1987) 381-386. | Zbl 0628.76110
and ,[20] Differentiation with respect to the domain in boundary value problems. Numer. Funct. Anal. Optim. 2 (1980) 649-687. | MR 619172 | Zbl 0471.35077
,[21] Introduction to shape optimization. Springer-Verlag, Berlin (1992). | MR 1215733 | Zbl 0761.73003
and ,