Some remarks on optimal insulation with Robin boundary conditions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913523331760128 |
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| author | Della Pietra, Francesco Oliva, Francescantonio |
| author_facet | Della Pietra, Francesco Oliva, Francescantonio |
| contents | We consider an optimal insulation problem of a given domain in $\mathbb R^N$. We study a model of heat trasfer determined by convection; this corresponds, before insulation, to a Robin boundary value problem. We deal with a prototype which involves the first eigenvalue of an elliptic differential operator. Such optimization problem, if the convection heat transfer coefficient is sufficiently large and the total amount of insulation is small enough, presents a symmetry breaking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20155 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks on optimal insulation with Robin boundary conditions Della Pietra, Francesco Oliva, Francescantonio Analysis of PDEs 49J45, 35J25, 35B06, 49R05 We consider an optimal insulation problem of a given domain in $\mathbb R^N$. We study a model of heat trasfer determined by convection; this corresponds, before insulation, to a Robin boundary value problem. We deal with a prototype which involves the first eigenvalue of an elliptic differential operator. Such optimization problem, if the convection heat transfer coefficient is sufficiently large and the total amount of insulation is small enough, presents a symmetry breaking. |
| title | Some remarks on optimal insulation with Robin boundary conditions |
| topic | Analysis of PDEs 49J45, 35J25, 35B06, 49R05 |
| url | https://arxiv.org/abs/2409.20155 |