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2006 | 4 | 4 | 573-584
Tytuł artykułu

An existence result for an interior electromagnetic casting problem

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
4
Strony
573-584
Opis fizyczny
Daty
wydano
2006-12-01
online
2006-12-01
Twórcy
autor
autor
Bibliografia
  • [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.
  • [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
  • [3] M. Barkatou:: Some geometric properties for a class of non Lipschitz-domains, New York J. of Math, Vol. 8, (2002), pp. 189–213.
  • [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
  • [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] 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] J. Decloux: On the two-Dimensional Magnetic Shaping Problem Without Surface tension, Ecole Polytechnique Fédérale de Lausanne, Suisse, 1990.
  • [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] D. Gilbarg and N.S. Trudinger: Elliptic partial equations of second order, Springer-Verlag, 1983.
  • [10] M. Hayouni and A. Novruzi: “Sufficient condition for existence of solution of a free boundary problem”, Quart. Appl. Math., to appear.
  • [11] A. Henrot: “Continuity with respect to the domain for the laplacian: a survey”, Control and Cybernetics, Vol. 23(3), (1994), pp. 427–443.
  • [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
  • [13] A. Henrot and M. Pierre: “About Existence of Equilibrium in Electromagnetic Casting”, Quater. Appl. Math., Vol. XLIX, (1991), pp. 563–575.
  • [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] 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] 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] 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] A. Novruzi: Contribution en optimisation de formes et Applications, Thesis(PhD), Université Henri Poincaré Nancy, 1997.
  • [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] 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0026-5
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