LYAPUNOV-TYPE INEQUALITY for EXTREMAL PUCCI'S EQUATIONS

In this article, we establish a Lyapunov-type inequality for the following extremal Pucci's equation: (M+λ, Λ (D2u) + b(x)|Du| + a(x)u = 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝN, N≥2. This work generalizes the well-known works on the Lyapunov inequality for extremal Pucci's equations with gradient nonlinearity.