Pointwise A Priori Estimates for Solutions to Some p-Laplacian Equations

In this article,we apply blow-up analysis to study pointwise a priori estimates for some p-Laplacian equations based on Liouville type theorems.With newly developed analysis techniques,we first extend the classical results of interior gradient estimates for the harmonic function to that for the p-harmonic function,i.e.,the solution ofΔpu=0,x∈Ω.We then obtain singularity and decay estimates of the sign-changing solution of Lane-Emden-Fowler type p-Laplacian equation-Δp^(u)=|u|^(λ-1)u,x∈Ω,which are then extended to the equation with general right hand term f(x,u)with certain asymptotic properties.In addition,point wise estimates for higher order derivatives of the solution to Lane-Emden type p-Laplacian equation,in a case of p=2,are also discussed.