Report
On the spectral instability for weak intermediate triharmonic problems
| العنوان: | On the spectral instability for weak intermediate triharmonic problems |
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| المؤلفون: | Ferraresso, Francesco |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Spectral Theory, 35J30 35J58 35P99 |
| الوصف: | We define the weak intermediate boundary conditions for the triharmonic operator $- \Delta^3$. We analyse the sensitivity of this type of boundary conditions upon domain perturbations. We construct a perturbation $(\Omega_\epsilon)_{\epsilon > 0}$ of a smooth domain $\Omega$ of $\mathbb{R}^N$ for which the weak intermediate boundary conditions on $\partial \Omega_\epsilon$ are not preserved in the limit on $\partial \Omega$, analogously to the Babu\v{s}ka paradox for the hinged plate. Four different boundary conditions can be produced in the limit, depending on the convergence of $\partial \Omega_\epsilon$ to $\partial \Omega$. In one particular case, we obtain a ``strange'' boundary condition featuring a microscopic energy term related to the shape of the approaching domains. Many aspects of our analysis could be generalised to an arbitrary order elliptic differential operator of order $2m$ and to more general domain perturbations. Comment: accepted for publication in 'Mathematical Methods in the Applied Sciences' |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1002/mma.8144 |
| URL الوصول: | http://arxiv.org/abs/2201.07636 |
| رقم الانضمام: | edsarx.2201.07636 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1002/mma.8144 |
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