Positivity preserving property for a class of biharmonic elliptic problems

The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds. We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 229; no. 1; pp. 1 - 23
Main Authors Berchio, Elvise, Gazzola, Filippo, Mitidieri, Enzo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2006
Subjects
35B50
47A75
35J40
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Summary:The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds. We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum of this operator exhibits some unexpected features: radial data may generate nonradial solutions. These boundary conditions are also of some interest in semilinear equations, since they enable us to give explicit radial singular solutions to fourth order Gelfand-type problems.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2006.04.003