An overview of unconstrained free boundary problems.
In this paper, we present a survey concerning unconstrained free boundary problems of type [Formula: see text] where B1 is the unit ball, Ω is an unknown open set, F(1) and F(2) are elliptic operators (admitting regular solutions), and [Formula: see text] 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.
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-1202, USA henriksh@math.kth.se.
Alessio
A
Figalli
Department of Mathematics, KTH Royal Institute of Technology, Stockholm 100 44, Sweden.
Henrik
H
Shahgholian
free boundary problems; matching data; obstacle-type; optimal regularity