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

/ Authors

/ Abstract

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

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

/ Authors

Yamin Wang, Huichang Yu

/ Abstract

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