Abstract
In this paper, we consider elliptic estimates for a system with smooth variable coefficients on a domain \({\Omega \subset \mathbb{R}^n,\, n \ge 2}\) containing the origin. We first show the invariance of the estimates under a domain expansion defined by the scale that \({y = Rx,\, x,\,y \in \mathbb{R}^n}\) 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.
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This paper was supported in part by research funds of Chonbuk National University in 2007.
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Cho, Y., Ozawa, T. & Shim, YS. Elliptic estimates independent of domain expansion. Calc. Var. 34, 321–339 (2009). https://doi.org/10.1007/s00526-008-0186-1
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DOI: https://doi.org/10.1007/s00526-008-0186-1