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The numerical approximation of the minimum problem: , is considered, where . The solution to this problem is a set with prescribed mean curvature and contact angle at the intersection of with . The functional is first relaxed with a sequence of nonconvex functionals defined in which, in turn, are discretized by finite elements. The -convergence of the discrete functionals to as well as the compactness of any sequence of discrete absolute minimizers are proven.
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