Elliptic estimates independent of domain expansion

Yonggeun Cho, Tohru Ozawa, Yong Sun Shim

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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 languageEnglish
Pages (from-to)321-339
Number of pages19
JournalCalculus of Variations and Partial Differential Equations
Volume34
Issue number3
DOIs
Publication statusPublished - 2009 Mar 1

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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