An existence result for an interior electromagnetic casting problem

 Access to full text

 Full (PDF)

1. [1] M. Barkatou: “Sufficient condition of existence for a free boundary problem for the p-Laplacian”, Ann. Sci. Math. Québec, Vol. 26(2), (2002), pp. 123–132. Zbl1054.35141
2. [2] M. Barkatou: D. Seck and I. Ly: “An existence result for a quadrature surface free boundary problem”, Centr. Eur. J. Math., Vol. 3(1), (2005), pp. 39–57, to appear. http://dx.doi.org/10.2478/BF02475654 Zbl1207.35106
3. [3] M. Barkatou:: Some geometric properties for a class of non Lipschitz-domains, New York J. of Math, Vol. 8, (2002), pp. 189–213. Zbl1066.35028
4. [4] D. Bucur and P. Trebeschi: “Shape Optimization Problems Governed by Nonlinear State Equations”, Proc. Roy. Sc. Edinburgh, Vol. 128A, (1998), (1998), pp. 945–963 Zbl0918.49030
5. [5] D. Chenais: “On the existence of a solution in a domain identification problem”, J. Math. Anal. Appl., Vol. 52, (1975), pp. 189–289. http://dx.doi.org/10.1016/0022-247X(75)90091-8 
6. [6] R. Dautray and J.L. Lions: Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. I et II, Masson, Paris, 1984. 
7. [7] J. Decloux: On the two-Dimensional Magnetic Shaping Problem Without Surface tension, Ecole Polytechnique Fédérale de Lausanne, Suisse, 1990. 
8. [8] E. Dibenedetto:: “C 1+α local regularity of weak solutions of degenerate elliptic equations”, Nonlinear Analysis., Vol. 7, (1983), pp. 827–850. http://dx.doi.org/10.1016/0362-546X(83)90061-5 
9. [9] D. Gilbarg and N.S. Trudinger: Elliptic partial equations of second order, Springer-Verlag, 1983. Zbl0562.35001
10. [10] M. Hayouni and A. Novruzi: “Sufficient condition for existence of solution of a free boundary problem”, Quart. Appl. Math., to appear. Zbl1054.35146
11. [11] A. Henrot: “Continuity with respect to the domain for the laplacian: a survey”, Control and Cybernetics, Vol. 23(3), (1994), pp. 427–443. Zbl0822.35029
12. [12] A. Henrot and M. Pierre: “About Critical Points of The Energy in an Electromagnetic Shaping Problem”, In: J.P. Zolésio (Ed): Lecture Notes in Control and Information Sciences, Boundary Control and Boundary Variation, Vol. 178, Sophia Antipolis, 1991, pp. 238–252 Zbl0820.35139
13. [13] A. Henrot and M. Pierre: “About Existence of Equilibrium in Electromagnetic Casting”, Quater. Appl. Math., Vol. XLIX, (1991), pp. 563–575. Zbl0731.76092
14. [14] M.V. Keldyš: “On the solvability and the stability of the Dirichlet problem”, Amer. Math. Soc. Trans., Vol. 2–51, (1966), pp. 1–73. 
15. [15] J.L. Lewis: Regularity of the derivatives of solutions to certain degenerate elliptic equations., Indiana Univ. Math. J., Vol. 32, (1983), pp. 849–858. http://dx.doi.org/10.1512/iumj.1983.32.32058 
16. [16] G.M. Lieberman: “Boundary regularity for solutions of degenerate elliptic equations”, Nonlinear Anal., Vol. 12, (1988) pp. 1203–1219. http://dx.doi.org/10.1016/0362-546X(88)90053-3 
17. [17] F. Murat and J. Simon: “Quelques résultats sur le contrôle par un domaine géométrique”, Publ. du labo. d’Anal. Num., Paris VI, (1974) pp. 1–46. 
18. [18] A. Novruzi: Contribution en optimisation de formes et Applications, Thesis(PhD), Université Henri Poincaré Nancy, 1997. 
19. [19] J. Sokolowski and J.P. Zolesio: Introduction to shape optimization: shape sensitity analysis, Springer Series in Computational Mathematics, Vol. 10, Springer, Berlin, 1992. 
20. [20] P. Tolksdorf: “On the Dirichlet problem for quasilinear equations in domains with conical boundary points”, Comm. Partial Differential Equations, Vol. 8(7), (1983), pp. 773–817. Zbl0515.35024