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

作     者：Xiao Qiang SUN Ji Guang BAO Xiao Qiang SUN;Ji Guang BAO

作者机构：School of MathematicsSun Yat-sen UniversityGuangzhou 510275P.R.China School of Mathematical SciencesBeijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第12期

页      面：2150-2162页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：Priori estimates Blow-up analysis p-Laplacian 

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 *** 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 *** 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.