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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
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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.
出处 《数学年刊(A辑)》 CSCD 北大核心 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
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 X-elliptic operators Green function Hole-filling technique Morrey's lemma Local H(o|¨)lder continuity
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