This paper is devoted to the solution of shape re problems by a level set method. The basi motivation for the setup of this level set algorithm is the well-studied method of asymptoti regularization, whi has been developed for ill-posed problems in Hilbert spa. Using analogies to this method, the ≠ analysis of the proposed level set method is established, it is shown that the evolving level set to a solution in the symmetri dieren≠ metri as the arti time evolves to innity. Fur-thermore, the regularizing properties of the level set method are shown, if the dis prin iple is used as a stopping rule. The numeri implementation of the level set method is dis and applied to some examples in order to the numeri results with theoreti statements. The numeri results demonstrate the power of the level-set, in parti for examples where the number of the solution of is not known a-priorly.
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Martin Burger (2001) studied this question.