Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem

Abstract

For the fully nonlinear Alt-Phillips problem with parameter ${\hat{I}}^3\in (1,2)$, we show that the free boundary intersects the fixed boundary tangentially where the Dirichlet data vanish. For this range of ${\hat{I}}^3$, this result is new even when the operator is the Laplacian.