In this paper, we prove H 2+α regularity for viscosity solutions to non-convex fully nonlinear parabolic equations near the boundary. This constitutes the parabolic counterpart of a similar C 2,α regularity result due to Silvestre and Sirakov proved in [15] for solutions to non-convex fully nonlinear elliptic equations.
In this article, we establish Lyapunov type inequality for the following extremal Pucci's equationwhere Ω is a smooth bounded domain in R N , N ≥ 2. This works generalize the well-known works on Lyapunov inequalities to fully nonlinear elliptic equations.
In this paper, we establish the existence of a positive solution to − M + λ,Λ (D 2 u) + H(x, Du) = k(x)f (u) u α in Ω, u > 0 in Ω, u = 0 on ∂Ω, under certain conditions on k, f and H, using viscosity sub-and supersolution method. The main feature of this problem is that it has singularity as well as a superlinear growth in the gradient term. We use Hopf-Cole transformation to handle the superlinear gradient term and an approximation method combined with suitable stability result for viscosity solution to outfit the singular nonlinearity. This work extends and complements the recent works on elliptic equations involving singular as well as superlinear gradient nonlinearities.
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