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

2020/04/08 by Elvise Berchio, Berchio, E., Alessio Falocchi +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2004.03862

openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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