Inserted: 28 jan 2015
Last Updated: 3 jul 2015
Journal: Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
In this paper we present a survey concerning unconstrained free boundary problems. Our main objective is to discuss a unifying approach to the optimal regularity of solutions to the matching problems, and list several open problems in this direction.