The two-sided stefan problem with a spatially dependent latent heat

We prove existence and uniqueness of solutions to a problem which generalizes the two-sided Stefan problem. The initial temperature distribution and variable latent heat may be given by positive measures rather than point functions, and the free boundaries which result are essentially arbitrary increasing functions which need not exhibit any degree of smoothness in general. Nevertheless, the solutions are “classical” in the sense that all derivatives and boundary values have the classical interpretation. We also study connections with the Skorohod embedding problem of probability theory and with a general class of optimal stopping problems.