TITLE

Elliptic estimates independent of domain expansion

AUTHOR(S)
Cho, Yonggeun; Ozawa, Tohru; Shim, Yong-Sun
PUB. DATE
March 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Mar2009, Vol. 34 Issue 3, p321
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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.
ACCESSION #
35948213

 

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