加权Sobolev空间和非线性椭圆型方程组

Weighted Sobolev Space and Nonlinear Elliptic Systems

本文研究高阶非线性椭圆方程组解集的致密性,其中w(x)允许有奇点。为此,我们引进了加权Sobolev空间H^m(w_0,w_1,…w_m,n),并证明了H^m(W_0,W_1,…w_m,闽),的Rellich紧性定理,W_0,W_1,……W_m∈A_2,A_2是Muckenhoupt权函数类。

Some pre-compactness theorems are studied for the solutions of the following higher ordernonlinear clliptic systems:hcrc w(x) is permitted to have singular points. For this purpose we introduce the weighted space Hm(w0,…wm,Ω) and prove a Rcllicb compactness theorem for it ,where wiEEE A2, Muckenhoupt’s class.