Physical interpretation and further properties of Robin capacity

In previous papers [4, 5, 3, 2], we have developed some properties of Robin capacity, showing in particular that it gives the sharp lower bound on capacity of the image of a subset of the boundary under normalized conformal mapping. Analogous studies [17, 18] have been made of the maximal capacity, the corresponding upper bound. We now continue these investigations by providing a physical interpretation of Robin capacity in terms of minimum energy, and we point out some additional properties.