Abstract

This paper deals with the existence and the regularity of state function u in an N-dimensional shape optimization problem. We use a variational approach to get the existence of a solution u of a variational problem. Then we prove a Lipschitz continuity result of u by a penalization argument

Author information

Contact details are reproduced from the original publication and may be historical.

Mohammed Hayouni

Université Henri Poincaré, Institut Elie Cartan, 54506 Vandœuvre-lès-Nancy, France
and: UMR CNRS 9973, Vandœuvre-lès-Nancy, France

References

  1. H. Berestycki, L. A. Caffarelli, L. Nirenberg: Uniform estimates for regularization of free boundary problems, Analysis and Partial Differential Equations, Coll. Pap. dedic. Mischa Cotlar, Lect. Notes Pure Appl. Math. 122 (1990) 567-619.Google Scholar
  2. G. Buttazzo, G. Dal Maso: An existence result for a class of shape optimization problems, Arch. Ration Mech. Anal. 122 (1993) 183-195.https://doi.org/10.1007/BF00378167Google Scholar
  3. M. Crouzeix: Variational approach of magnetic shaping problem, Eur. Jour. of Mechanics 10(5) (1991) 527-536.Google Scholar
  4. D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983.Google Scholar
  5. M. Hayouni: Existence et régularité pour des problèmes d'optimisation de formes, Thèse de l'Université Henri Poincaré Nancy 1, 1997.Google Scholar
  6. A. Henrot, M. Pierre: About existence of equilibria in electromagnetic casting, Quarterly of Applied Math. 49(3) (1991) 563-575.https://doi.org/10.1090/qam/1121687Google Scholar
  7. E. Sperner: Symmetrisierung für Funktionen mehrerer Variablen, Man. Math. (1974) 159-170.https://doi.org/10.1007/BF01184955Google Scholar

Suggested citation

M. Hayouni. “Lipschitz Continuity of the State Function in a Shape Optimization Problem.” Journal of Convex Analysis 6 (1999), No. 1, 71–90. https://doi.org/10.68381/jca06006

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 1999. Rights now held by Banach Press.