中文摘要：

利用Moser-Nash迭代和稠密引理，得到了在自然增长下的非线性退化椭圆方程有界弱解具有某一Hoelder指数的正则性；在已知数据的进一步正则性下，建立了具有任意γ满足0≤γ〈κ的优化Hoelder连续性指数，其中κ是A-调和函数的局部Hoel der连续指数．

英文摘要：

It＇s established that the bounded weak solution of a class of nonlinear degenerate elliptic equations with the natural growth belongs to the HSlder space with some Hoelder exponent by way of Moser-Nash＇s iterating argument and a density lemma. Then, we further obtain that each bounded weak solution is of sharp Hoelder exponent with any γ ： 0 ≤ γ 〈 κ under the additional data regularity assumptions, where κ is just as the local HSlder index of A-harmonic functions.