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Journal of Convex Analysis 06 (1999), No. 1, 071--090
Copyright Heldermann Verlag 1999

Lipschitz Continuity of the State Function in a Shape Optimization Problem

Mohammed Hayouni
Université Henri Poincaré, Institut Elie Cartan, 54506 Vandoevre-les-Nancy, France

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.

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