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

作　　者：Xiao Qiang SUN Ji Guang BAO 

机构地区：[1]School of Mathematics,Sun Yat-sen University,Guangzhou 510275,P.R.China [2]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第12期2150-2162,共13页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11871070 and 62273364);the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B151502120)。

摘　　要：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.

关 键 词：Priori estimates Blow-up analysis P-LAPLACIAN 

分 类 号：O175[理学—数学]