We study the properties of the minima of the functional $$F_\lambda \left( E \right) = P\left( E \right) + \lambda |\Omega \backslash E|, E \subset \Omega $$ with λ∈(0,+∞). We discuss a result of approximation of sets having finite perimeter and other applications to problems of capillarity and segmentation of images in computer vision.
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