Elliptic estimates independent of domain expansion

Yonggeun Cho; Tohru Ozawa; Yong Sun Shim

doi:10.1007/s00526-008-0186-1

Elliptic estimates independent of domain expansion

Yonggeun Cho^*, Tohru Ozawa, Yong Sun Shim

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	321-339
Number of pages	19
Journal	Calculus of Variations and Partial Differential Equations
Volume	34
Issue number	3
DOIs	https://doi.org/10.1007/s00526-008-0186-1
Publication status	Published - 2009 Mar 1
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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AU - Ozawa, Tohru

AU - Shim, Yong Sun

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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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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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Elliptic estimates independent of domain expansion

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