On domain decomposition for elliptic systems

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Abstract

We consider a region unbounded in at least one direction on which is defined an abstract elliptic system subject to non-homogeneous Neumann data on part (Formula presented.) of the surface that is otherwise free. We show that a quadratic form, analogous to the Dirichlet integral, becomes increasingly small on sub-regions increasingly remote from (Formula presented.). The technique is illustrated by various specific linear and nonlinear examples, including the p-Laplacian, for some of which the method must be slightly modified.

Original languageEnglish
Pages (from-to)803-822
Number of pages20
JournalJournal of Dynamics and Differential Equations
Volume27
Issue number3
Early online date26 Aug 2014
DOIs
Publication statusPublished - Dec 2015

Keywords

  • Domain decomposition
  • Edge effects
  • Elliptic systems
  • Saint-Venant's principle

ASJC Scopus subject areas

  • Analysis

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