We investigate the existence, asymptotic boundary behavior and uniqueness of viscosity solutions u ∈ C0(Ω) of equations \({\cal{M}}_{\mathbf{a}}(D^{2}u)=f(u)+h(x)\) in Ω ⊂ ℝn such that u(x) → ∞ as x → ∂Ω. Such solutions are referred to as large or boundary blow-up solutions. Here, Ω is a smooth bounded domain, \({\cal{M}}_{\mathbf{a}}\) is a weighted partial trace operator, f is a non-decreasing function that satisfies the Keller–Osserman condition, and h is a continuous function in Ω. The main difficulty in the investigation rests on the possibility that \({\cal{M}}_{\mathbf{a}}\) is very degenerate elliptic, and h is unbounded as well as sign-changing in Ω. To the best of our knowledge, large solutions to equations involving partial trace operators have not been investigated before.
