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The aim of this paper is to develop a functional-analytic framework for the constructionof level set methods, when applied to shape optimization and shape reconstructionproblems. As a main tool we use a notion of gradient flows for geometric configurationssuch as used in the modelling of geometric motions in materials science. The analogiesto this field lead to a scale of level set evolutions, characterized by the norm used for thechoice of the velocity. This scale of methods also...

A framework for the construction of level set methods for shape optimization and reconstruction