A Priori Estimates in Nonlinear Eigenvalue Problems for Elliptic Systems

Research output: Contribution to journalArticle

Abstract

The systems considered have the form {black small square} in Ω, {black small square} on ∂Ω, where {black small square} is a bounded domain, A is a matrix of second order elliptic operators, and γ is a real parameter. For simplicity the results are stated for a single equation, but the range of validity for systems is discussed. The first type of a priori estimates give lower bounds for sup {black small square} in terms of γ and |Ω| when {black small square} is superlinear, upper bounds for sup {black small square} when {black small square} is sublinear, and lower bounds for γ when {black small square} has linear growth. The second type of estimates generalize to systems results of Brezis and Turner and P. L. Lions for single equations; they give upper bounds for sup {black small square} in the superlinear case. Those estimates require A to be diagonal. None of the results require a variational structure for the system.

Original languageEnglish (US)
Pages (from-to)123-129
Number of pages7
JournalNorth-Holland Mathematics Studies
Volume92
Issue numberC
DOIs
StatePublished - 1984

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Nonlinear Eigenvalue Problem
Elliptic Systems
A Priori Estimates
Lower bound
Upper bound
Elliptic Operator
Estimate
Bounded Domain
Simplicity
Generalise

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A Priori Estimates in Nonlinear Eigenvalue Problems for Elliptic Systems. / Cosner, George.

In: North-Holland Mathematics Studies, Vol. 92, No. C, 1984, p. 123-129.

Research output: Contribution to journalArticle

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