In this paper, we consider elliptic estimates for a system with smooth variable coefficients on a domain Ω ⊆ 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 \in R 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.
|Number of pages||19|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2009 Mar 1|
ASJC Scopus subject areas
- Applied Mathematics