A General Class of Unconstrained Free Boundaries
نویسندگان
چکیده
In this paper we present a survey concerning unconstrained free boundary problems of type F1(D u,∇u, u, x) = 0 in B1 ∩ Ω, F2(D u,∇u, u, x) = 0 in B1 \ Ω, u ∈ S(B1), where B1 is the unit ball, Ω is an unknown open set, F1, F2 are elliptic operators (admitting regular solutions), and S is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solutions to the above matching problems, and list several open problems in this direction.
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