Calculus of Variations and Geometric Measure Theory
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E. Berchio - F. Gazzola - E. Mitidieri

Positivity preserving property for a class of biharmonic elliptic problems

created by gazzola on 16 Sep 2005


Submitted Paper

Inserted: 16 sep 2005

Year: 2005


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.


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