The two-phase fractional obstacle problem

Mark Allen, Erik Lindgren, Arshak Petrosyan

We study minimizers of the functional $${\int }_{B_1^{+}}|\nabla u{|}^2{x}_n^{a}dx+2{\int }_{B_1^{\prime }}({\lambda }_{+}{u}^{+}+{\lambda }_{-}{u}^{-})d{x}^{\prime },$$ for $a\in (-1,1)$. The problem arises in connection with heat…