Sign-Definite Solutions in Some Linear Elliptic Systems

Chris Cosner, Philip W. Schaefer

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We consider a weakly coupled set of two partial differential equations where the coupling matrix has variable elements and the principal part of each equation is the same uniformly elliptic operator. We obtain necessary conditions that the system of equations can be decoupled. By decoupling the system and using a positivity lemma due to Hess and Kato, we determine the algebraic sign of the solution components. This work extends recent results of de Figueiredo and Mitidieri. Further, one can use these results to determine the sign of the solution to certain fourth order elliptic boundary value problems.

Original languageEnglish (US)
Pages (from-to)347-358
Number of pages12
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume111
Issue number3-4
DOIs
StatePublished - 1989

ASJC Scopus subject areas

  • Mathematics(all)

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