Shape derivative in the wave equation with Dirichlet boundary conditions

The aim of this paper is to give a full analysis of the the shape different iability for the solution to the second order hyperbolic equation with Diri chlet boundary conditions. The implicit function theorem does not work to s olve the problem of weak regularity of the data; nevertheless by a more tec hnical approach we prove an analogous result. We will first prove the theor em under strong regularity of the right hand side, then using the hidden re gularity we will prove the shape derivative continues to exist under weak c ondition of regularity. We end up with a second order shape derivative for this problem. (C) 1999 Academic Press.