An overview of unconstrained free boundary problems

• In this paper, we present a survey concerning unconstrained free boundary problems of type F-1(D(2)u, del u, u, x) = 0 in B-1 boolean AND Omega, F-2(D(2)u, del u, u, x) = 0 in B-1 \ Omega, u is an element of S(B-1), where B-1 is the unit ball, Omega is an unknown open set, F-1 and F-2 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

free boundary problems

obstacle-type

optimal regularity

matching data

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)