Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Sufficient condition for the existence of solutions of a free boundary problem

Authors: Mohammed Hayouni and Arian Novruzi
Journal: Quart. Appl. Math. 60 (2002), 425-435
MSC: Primary 35R35; Secondary 35J20
DOI: https://doi.org/10.1090/qam/1914434
MathSciNet review: MR1914434
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Abstract: In this paper we study the existence of critical points of a functional depending on $ \Omega \subset \mathbb{R}^{2}$ through its perimeter and the solution of the Dirichlet problem in $ \Omega $, under the constraint that the measure of $ \Omega $ is given. We give a sufficient condition for the existence of critical points using the implicit function theorem.

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  • [1] J. Descloux, On the two-dimensional magnetic shaping problem without surface tension, Ëcole Polytechnique Fédérale de Lausanne, Suisse, 1990
  • [2] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983 MR 737190
  • [3] A. Henrot and M. Pierre, About critical points of the energy in an electromagnetic shaping problem, Lecture Notes in Control and Information Sciences, J. P. Zolésio (Ed.), Boundary Control and Boundary Variation, 178, Sophia Antipolis, 1991, pp. 238-252 MR 1173448
  • [4] A. Henrot and M. Pierre, About existence of equilibria in electromagnetic casting, Quarterly of Applied Mathematics, XLIX(3), 563-575 (1991) MR 1121687
  • [5] A. Henrot and M. Pierre, Un problème inverse en formage des métaux liquides, Mathematical Modelling and Numerical Analysis, 23, 155-177 (1989) MR 1015924
  • [6] A. Novruzi, Contribution en Optimisation de Formes et Applications, Ph.D. Thesis, Université Henri Poincaré Nancy 1, 1997
  • [7] J. Simon, Differentiation with respect to the domain in boundary value problems, Numerical Functional Analysis and Optimization, 2(7&8), 649-687 (1980) MR 619172
  • [8] J. Sokolowski and J. P. Zolesio, Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer-Verlag, New York, 1992 MR 1215733

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DOI: https://doi.org/10.1090/qam/1914434
Article copyright: © Copyright 2002 American Mathematical Society

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