Elliptic estimates independent of domain expansion

Abstract

In this paper, we consider elliptic estimates for a system with smooth variable coefficients on a domain Omega subset of R(n), n >= 2 containing the origin. We first show the invariance of the estimates under a domain expansion defined by the scale that y = Rx, x, y is an element of R(n) 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.