TY - JOUR
T1 - Elliptic estimates independent of domain expansion
AU - Cho, Yonggeun
AU - Ozawa, Tohru
AU - Shim, Yong Sun
PY - 2009/3/1
Y1 - 2009/3/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-008-0186-1
DO - 10.1007/s00526-008-0186-1
M3 - Article
AN - SCOPUS:58149347789
SN - 0944-2669
VL - 34
SP - 321
EP - 339
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
ER -