X-椭圆方程弱解Hlder连续性的Green函数法  

An Application of Green Function to Interior Hlder Continuity of Weak Solutions to X-Elliptic Equations

作　　者：郑神州[1] 卢寒芳[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《数学年刊（A辑）》2010年第3期295-304,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10671022)资助的项目

摘　　要：应用线性X-椭圆算子的Green函数与次Laplace算子基本解的局部比较原理,建立了具有有界可测系数散度型X-椭圆方程弱解的局部H(o|¨)lder连续性.以Green函数为核函数,通过holefilling技巧得到弱解满足Morrey引理条件,从而建立正则性结果,这在某种意义下取代了经典的DeGiorgi-Moser-Nash迭代技术.According to the comparison principle of Green function of X-elliptic operator with Laplacian in recent Mazzoni＇s paper,the local Holder continuity of weak solutions to X-elliptic equations with bounded measurable coefficients is established.Instead of De Giorgi-Moser-Nash iterating technique,the authors obtain that the weak soluiton must satisfy the assumption of Morrey＇s lemma by making use of Green function as a kernel function and the so-called hole-filling argument.

关 键 词：X-椭圆算子 GREEN函数 Hole-filling方法 Morrey引理 局部H(o|¨)lder连续 

分 类 号：O175.25[理学—数学]