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.
Positivity preserving property for a class of biharmonic elliptic problems / Berchio, Elvise; F., Gazzola; E., Mitidieri. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 229:(2006), pp. 1-23. [10.1016/j.jde.2006.04.003]
Positivity preserving property for a class of biharmonic elliptic problems
BERCHIO, ELVISE;
2006
Abstract
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.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2522493
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