Elliptic estimates independent of domain expansion

In this paper, we consider elliptic estimates for a system with smooth variable coefficients on a domain containing the origin. We first show the invariance of the estimates under a domain expansion defined by the scale that with parameter R > 1, provided that the coefficients are in a homogeneous Sobolev space. Then we apply these invariant estimates to the global existence of unique strong solutions to a parabolic system defined on an unbounded domain. This paper was supported in part by research funds of Chonbuk National University in 2007.