Let $x_1,\ldots,x_n$ be $n \ge 1$ distinct points in $\mathbb R^d$ and consider two discrete distributions on these points $\mu = (1/n)\sum_{i=1}^n\delta_{x_i}$, and $\nu = \sum_{i=1}^n\nu_i\delta_{x_i}$ with $\nu_1,\ldots,\nu_n \ge 0$ and $\sum_i \nu_i = 1$.

Let $(x_i,x_j) \mapsto c(x_i,y_j)$ be a distance on the $n$ points $x_1,\ldots,x_n$. For example, $c(x_i,x_j) := \|x_i-x_j\|_p$ for some $p \in [1,\infty)$.

Question

What's a closed form formula for the Wasserstein distance between $\mu$ and $\nu$ ?