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Abstract:  We study the motion of the boundary of a set, where the velocity depends on the mean curvature and the normal derivative of the capacity potential of the set. We show that starting from smooth initial data one has a smooth flow for short time, and give an example where the smooth flow exists globally in time.

To study the flow after singularities, we propose two possible notions of weak solutions motivated by the comparison property and gradient flow structure of the smooth flow.