Has there been much work in the setting of Stefan (or general free boundary) problems with some type of nonlocality?
A search on Google and MathSciNet give me only a handful of results which greatly surprises me. Maybe I am searching with the wrong terms?
I'm mostly interested in well-posedness theory of solutions.
Neither do I know about work regarding general nonlocal free boundary problems nor nonlocal Stefan problems (perhaps because they classically are defined as local PDEs and it might be considered somewhat artificial to look at nonlocal versions). However, if you search for "fractional Laplacian and free boundary" you will get some hits, similar in numbers or perhaps slightly more than for the nonlocal Stefan problem.
