Boundary homogenization for a triharmonic intermediate problem

Arrieta, José M.; Ferraresso, Francesco; Lamberti, Pier Domenico (2018). Boundary homogenization for a triharmonic intermediate problem. Mathematical methods in the applied sciences, 41(3), pp. 979-985. Wiley 10.1002/mma.4025

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We consider the triharmonic operator subject to homogeneous boundary conditions of intermediate type on a bounded domain of the N‐dimensional Euclidean space. We study its spectral behaviour when the boundary of the domain undergoes a perturbation of oscillatory type. We identify the appropriate limit problems that depend on whether the strength of the oscillation is above or below a critical threshold. We analyse in detail the critical case that provides a typical homogenization problem leading to a strange boundary term in the limit problem.

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