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Journal of Convex Analysis, Vol. 6, No. 1, pp. 71-90 (1999)
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Lipschitz Continuity of the State Function in a Shape Optimization Problem

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Mohammed Hayouni

Université Henri Poincaré Nancy 1, Institut Elie Cartan, UMR CNRS 9973, B.P. 239, 54506 - Vando\!euvre-les-Nancy, France, hayouni@iecn.u-nancy.fr

**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.

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