临界增长拟线性椭圆方程的正则性

REGULARITY FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

近年来,非线性临界增长椭圆方程得到了广泛的研究.对于半线性方程,许多正则性结果已经得到.本文我们考虑拟线性方程-sum from i=sum from i=1 to N （?）/（（?）xi）（αi（x,u,▽u））=α（x,u,▽u）,x∈（?）（?）RN （1）的 W（?）,p（?）弱解的正则性.假定αi（x,z,q）,α（x,z,q）是（?）×R×RN 上的 Carathéodory 函数。

In this paper,we prove that the W^(1,p)solutions of the following quasilinear ellip-tic equation possess interior C^(?) regularity:-sum from i=1 to N (?)/((?)x_i)(|▽u|^(p-2)((?)u)/((?)x_i))=f(x,u),x∈Ω,where Q is a domain in R^N, N>p>1,and |f(x,u)|≤C(1+|u|^((NP)/(N-P)-1)) forany x∈Q,u∈R.