Université Henri Poincaré Nancy 1, Institut Elie Cartan, UMR CNRS 9973, B.P. 239, 54506 - Vando\!euvre-les-Nancy, France, email@example.com
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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