拟线性椭圆型方程与方程组非负解的一个先验估计  

A Priori Estimates for Nonnegative Solutions of the Quasilinear Elliptic Equations and Systems

作　　者：李振杰[1] 张正策[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049

出　　处：《应用数学学报》2014年第2期379-384,共6页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11371286);教育部回国留学人员基金资助项目

摘　　要：本文研究一类带有非线性源项及其扰动的椭圆型p-Laplace方程—div(|▽u|^(p-2)▽u)=u^q+f(x,t,u,▽u),其中p>2,q>p—1.对单个方程,证明了关于非负解及其梯度的一个先验估计;同时,对于含有两个方程的方程组,我们也得到了类似的估计.本文,我们主要应用了Doubling引理和关于椭圆方程与方程组的Liouville定理.In this paper, we consider the elliptic p-Laplace equation with nonlinear source and its perturbation -div（｜u｜p-2 u） = uq ＋ f（x, t, u, u）, where p 〉 2 and q 〉 p- 1. For this problem we prove an a priori estimates for both nonnegative solution and its gradient. Also we get the similar estimates of nonnegative solutions for the elliptic systems consisting of two equations. We mainly depend on the Doubling lemma and some known Louville-type theorems for elliptic equations and systems.

关 键 词：椭圆方程 椭圆方程组 p-Laplace 

分 类 号：O175.25[理学—数学]