Journal of convex analysis, Tome 6 (1999) no. 1, pp. 71-9
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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/
@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},
year = {1999},
volume = {6},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a5/}
}
TY - JOUR
AU - M. Hayouni
TI - Lipschitz Continuity of the State Function in a Shape Optimization Problem
JO - Journal of convex analysis
PY - 1999
SP - 71
EP - 9
VL - 6
IS - 1
UR - http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a5/
ID - JCA_1999_6_1_JCA_1999_6_1_a5
ER -
%0 Journal Article
%A M. Hayouni
%T Lipschitz Continuity of the State Function in a Shape Optimization Problem
%J Journal of convex analysis
%D 1999
%P 71-9
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a5/
%F JCA_1999_6_1_JCA_1999_6_1_a5
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.
