About stability of equilibrium shapes
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 4, pp. 811-834.
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Dambrine, Marc; Pierre, Michel. About stability of equilibrium shapes. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 4, pp. 811-834. http://www.numdam.org/item/M2AN_2000__34_4_811_0/

[1] J.-P. Brancher, J. Etay and O. Séro-Guillaume, Formage d'une lame métallique liquide. Calculs et expériences. J. Mec. Theor. Appl. 2 (1983) 977-989. | Zbl

[2] D. Bucur and J.-P. Zolésio, Anatomy of the Shape Hessian Via Lie Brackets. Ann. Mat. Pura Appl.(IV) CLXXIII (1997) 27-143. | MR | Zbl

[3] M. Crouzeix, Variational approach of a magnetic shaping problem. Eur. J. Mech. B Fluids 10 (1991) 527-536. | MR | Zbl

[4] M. Dambrine, Hessiennes de formes et stabilité de formes critiques. Ph.D. thesis, Université de Rennes 1, France (2000).

[5] R. Dautray and J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Tome 2. Masson, Paris (1985). | MR | Zbl

[6] M. Delfour and J.-P. Zolésio, Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian. SIAM Control Optim. 29 (1991) 1414-1442. | MR | Zbl

[7] J. Descloux, On the two dimensional magnetic shaping problem without surface tension. Report, Analysis and numerical analysis, 07.90, École Polytechnique Fédérale de Lausanne (1990).

[8] J. Descloux, 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 | Zbl

[9] J. Descloux, A stabihty resuit for the magnetic shaping problem. Z. Angew. Math. Phys. 45 (1994) 543-555. | MR | Zbl

[10] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Berlin, 2nd edn (1983). | MR | Zbl

[11] A. Henrot and M. Pierre, Stability in shaping problems. (to appear).

[12] A. Henrot and M. Pierre, 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 | Zbl

[13] A. Henrot and M. Pierre, Un problème inverse en formage des métaux liquides. RAIRO. Modél. Math. Anal. Numér. 23 (1989) 155-177. | EuDML | Numdam | MR | Zbl

[14] A. Henrot and M. Pierre, About critical points of the energy in the electromagnetic shaping problem, in Boundary Control and Boundary variations, Springer-Verlag, 178 (1991) 238-252. | MR | Zbl

[15] A. Henrot and M. Pierre, About existence of equilibria in electromagnetic casting. Quart. Appl. Math. 49 (1991) 563-575. | MR | Zbl

[16] F. Murat and J. Simon, Sur le contrôle par un domaine géométrique. Rapport du L.A. 189, Université Paris VI, France (1976).

[17] A. Novruzi, Contribution en Optimisation de Formes et Applications. Ph.D. thesis, Université Henri Poincaré, Nancy (1996).

[18] A. Novruzi and M. Pierre, Structure of Shape Derivatives. Prépublication IRMAR, n° 00-07, Rennes (2000).

[19] O. Séro-Guillaume and D. Bernardin, Note on a Hamiltonian formalism for the flow of a magnetic fluid with a free surface. J. Fluid Mech. 181 (1987) 381-386. | Zbl

[20] J. Simon, Differentiation with respect to the domain in boundary value problems. Numer. Funct. Anal. Optim. 2 (1980) 649-687. | MR | Zbl

[21] J. Sokolowski and J.-P. Zolésio, Introduction to shape optimization. Springer-Verlag, Berlin (1992). | MR | Zbl