Geodesic
Lipschitz Continuity of the State Function in a Shape Optimization Problem
Journal of convex analysis, Tome 6 (1999) no. 1, pp. 71-9.

Voir la notice de l'article provenant de la source Heldermann Verlag

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. 
@article{JCA_1999_6_1_JCA_1999_6_1_a5,
     author = {M. Hayouni},
     title = {Lipschitz {Continuity} of the {State} {Function} in a {Shape} {Optimization} {Problem}},
     journal = {Journal of convex analysis},
     pages = {71--9},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {1999},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a5/}
}
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M. Hayouni. Lipschitz Continuity of the State Function in a Shape Optimization Problem. Journal of convex analysis, Tome 6 (1999) no. 1, pp. 71-9. http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a5/