Free transmission problems (Q2346859)

The authors describe the notion of transmission problems using several examples like an ice melting process inside a second material. Also, they give an interesting overview on the corresponding literature. The main objective of the article under review is to provide a mathematical treatment of transmission problems including free boundaries of discontinuity. Realizing that strategy leads in a natural way to the study of local minima of some energy integral. The existence of \(L^{\infty}\) bounds of solutions can be established. Furthermore, it is proved by the authors that variational solutions are non-degenerate and a regularity theory for solutions of such free boundary problems is developed.