一类退缩椭圆方程组弱解的正则性

ON THE REGULARITY OF WEAK SOLUTIIONS TO A CLASS OFDEGENERATE ELLIPTIC SYSTEM

本文讨论一类散度型退缩椭圆方程组．通过引入Ｍｕｃｋｅｎｈｏｕｔ函数类，证明了退缩方程组的弱解在加权Ｓｏｂｏｌｅｖ空间中的局部正则性，即证明了：除了一个Ｈａｕｓｄｏｒｆ测度为零的奇点集之外，弱解几乎处处Ｈ¨ｏｌｄｅｔ连续．

This paper concerns with a class of degenerate elliptic system in diver divergence form.By introducing Muckenhout weighted function class,the paper proves the local regularity in the weighted Sobole space for weak solutions to degenerate elliiptic system,i.e. it is proved that almost everywhere Hlder continuity exists for weak solutions except a singular set in which Hausdorff measure is equivalent to zero.