自然增长下非线性退化椭圆方程的优化Hlder连续指数

Sharp Hlder Exponents for Nonlinear Degenerate Elliptic Equations with the Natural Growth

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Hlder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Hlder连续性指数,其中κ是A-调和函数的局部Hlder连续指数.

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.