An overview of unconstrained free boundary problems

作者：Figalli Alessio; Shahgholian Henrik^*

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2015, 373(2050): 20140281.

DOI：10.1098/rsta.2014.0281

• free boundary problems
• obstacle-type
• optimal regularity
• matching data

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.

• 出版日期2015-9-13