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Abstract: We study viscosity solutions for a degenerate one-phase free boundary problem of the form $Delta w = frac{h(
abla w)}{w}$. We assume the existence of a star-shaped domain $D$ such that $h < 0$ in $D$, $h = 0$ on $partial D$, and $h > 0$ in $bar{D}^{c}$. This type of degenerate one-phase free boundary problem arises when a canonical transformation is performed to a semilinear equation $Delta u = f(u)$, and $f$ morally behaves like $u^{-(gamma + 1)}$ for some $gamma > 0$. In this case, known as the Alt-Phillips equation for negative exponents, $h(
abla u) = c(|
abla u|^2 - 1)$. We show existence of a viscosity solution, Lipschitz regularity, and regularity of the free boundary at flat points. Additionally, we show that as $gamma$ degenerates to $2$, the free boundary becomes a minimal surface.