Time：14:00-16:00, Friday, September 25 2026
Venue：E14-301
Speaker：Yamin Wang, China Agricultural University
Abstract：Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem
Title：The classical Alt-Phillips problem, appearing in the study of permeable catalysts and population dynamics, was first studied by Phillips [1983] and Alt-Phillips [1986]. It embeds two of the most well studied elliptic free boundary problems as special cases, namely, the Alt-Caffarelli problem when the parameter $gamma=0$ and the obstacle problem when $gamma=1$.
In this talk, we study the boundary behavior of a solution to the fully nonlinear Alt-Phillips problem with $\gamma\in (1,2)$. We show that the free boundary intersects the fixed boundary tangentially where the Dirichlet data vanish. For this range of $\gamma$, our result is new even when the operator is the Laplacian. This is joint work with Yu Hui.
