# Elliptic estimates independent of domain expansion

Yonggeun Cho, Tohru Ozawa, Yong Sun Shim

Research output: Contribution to journalArticle

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 321-339 19 Calculus of Variations and Partial Differential Equations 34 3 https://doi.org/10.1007/s00526-008-0186-1 Published - 2009 Mar Yes

### Fingerprint

Sobolev spaces
Invariance
Estimate
Parabolic Systems
Strong Solution
Homogeneous Space
Unbounded Domain
Variable Coefficients
Global Existence
Sobolev Spaces
Invariant
Coefficient

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics

### Cite this

Elliptic estimates independent of domain expansion. / Cho, Yonggeun; Ozawa, Tohru; Shim, Yong Sun.

In: Calculus of Variations and Partial Differential Equations, Vol. 34, No. 3, 03.2009, p. 321-339.

Research output: Contribution to journalArticle

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