It is well known that for higher order elliptic equations, the positivity preserving property (PPP) may fail. In striking contrast to what happens under Dirichlet boundary conditions, we prove that the PPP holds for the biharmonic operator on rectangular domains under partially hinged boundary conditions, i.e., nonnegative loads yield positive solutions. The result follows by fine estimates of the Fourier expansion of the corresponding Green function.

A positivity preserving property result for the biharmonic operator under partially hinged boundary conditions

Falocchi A.
2021

Abstract

It is well known that for higher order elliptic equations, the positivity preserving property (PPP) may fail. In striking contrast to what happens under Dirichlet boundary conditions, we prove that the PPP holds for the biharmonic operator on rectangular domains under partially hinged boundary conditions, i.e., nonnegative loads yield positive solutions. The result follows by fine estimates of the Fourier expansion of the corresponding Green function.
Biharmonic
Green function
Partially hinged plate
Positivity preserving
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1194115
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