各向异性的椭圆方程障碍问题弱解的局部正则性(英文)

Local Regularityfor Weak Solutions of Anisotropic Obstacle Problems to Elliptic Equations

本文在适当的假设下研究各向异性的非线性椭圆方程-divA(x,Du)=B(x,u,Du),使用各向异性的逆Hlder不等式和Sobolev不等式,得到椭圆方程障碍问题的弱解的局部正则性,推广了A-调和方程-divA(x,Du)=0的相关结果.

This paper deals with anisotropic obstacle problems for nonlinear elliptic equation-divA（x,Du）=B（x,u,Du）.Under some suitable assumptions,a local regularity result is given by using an anisotropic reverse Hlder＇s inequality and Sobolev inequality,which can be regard as a generalization of the A-harmonic equation.