各向异性椭圆方程障碍问题弱解的拟最小化性质

Quasiminimization Property for Weak Solutions of Obstacle Problems of Anisotropic Elliptic Equations

拟最小化性质是研究椭圆方程弱解的重要工具。该文研究了各向异性的A-调和方程-divA(x,Du)=0障碍问题的弱解,使用了Hlder不等式,Young不等式以及一些基本不等式,完成了各向异性情形下弱解的积分估计,得到了各向异性障碍问题弱解的拟最小化性质。

Quasiminimization property is an important tool to study weak solutions of elliptic equations. This paper deals with weak solutions of anisotropic obstacle problems for A-harmonic equation-divA （ x, Du） = 0, a property of quasiminimization of weak solutions is obtained. In order to estimate the integral of weak solutions in anisotropic case, it applies Holder inequality and Young inequality as well as some basic inequalities.