带测度项的退缩椭圆方程弱解的正则性

Regularity for Degenerate Elliptic Equation Involving Measure

研究了退缩椭圆方程弱解的正则性，这里μ是一非负Ｒａｄｏｎ测度，１＜ｐ＜＋∞。Ｂ（ｘ，ｕ，ｈ）满足自然增长条件。证明了：如果μ满足增长条件，对所有Ｒ￣Ｎ中的球Ｂ（ｘ，ｒ）有μ［Ｂ（ｘ，ｒ）］≤Ｃｒ￣（Ｎ－ｐ＋ε）．（ε＞０）．那么μ是局部Ｈｏｌｄｅｒ连续的。

The regularity of weak solutions of degenerate elliptic equationwas investigated.Here μwas a nonnegative Radon mea-sure,1<p<+∞,B(x,u, h)satisfies the natural grouth condition. It was proved that u isHolder continnous if μ satisfies the grouth property μ[B(x,r)]≤Cr￣(N-p+ε)for all balls B(x,r) inR￣N.