Remarks on the reinforcement of the spectrum of an elliptic problem with Robin boundary condition
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| Format: | Preprint |
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2025
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| _version_ | 1866915922593185792 |
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| author | Cristoforoni, Emanuele Villone, Federico |
| author_facet | Cristoforoni, Emanuele Villone, Federico |
| contents | We investigate the spectral properties of a differential elliptic operator on $H^1(\barΩ\cup Σ)$, where $Ω$ is a smooth domain surrounded by a layer $Σ$. The thickness of the layer is given by $\varepsilon h$, where $h$ is a positive function defined on the boundary $\partial Ω$ and $\varepsilon$ is the ellipticity constant of the operator in $Σ$. We prove that, in the limit for $\varepsilon$ going to $0$, the spectrum converges to the spectrum of a differential elliptic operator in $H^1(Ω)$, and we investigate a first-order asymptotic development. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on the reinforcement of the spectrum of an elliptic problem with Robin boundary condition Cristoforoni, Emanuele Villone, Federico Analysis of PDEs Spectral Theory 35P20, 49R05, 35J25, 80A19 We investigate the spectral properties of a differential elliptic operator on $H^1(\barΩ\cup Σ)$, where $Ω$ is a smooth domain surrounded by a layer $Σ$. The thickness of the layer is given by $\varepsilon h$, where $h$ is a positive function defined on the boundary $\partial Ω$ and $\varepsilon$ is the ellipticity constant of the operator in $Σ$. We prove that, in the limit for $\varepsilon$ going to $0$, the spectrum converges to the spectrum of a differential elliptic operator in $H^1(Ω)$, and we investigate a first-order asymptotic development. |
| title | Remarks on the reinforcement of the spectrum of an elliptic problem with Robin boundary condition |
| topic | Analysis of PDEs Spectral Theory 35P20, 49R05, 35J25, 80A19 |
| url | https://arxiv.org/abs/2509.22305 |