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| Format: | Preprint |
| Published: |
2022
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| Online Access: | https://arxiv.org/abs/2202.12089 |
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| _version_ | 1866908981242363904 |
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| author | Ma, Linjie |
| author_facet | Ma, Linjie |
| contents | In high-contrast composite materials, the electric (or stress) field may blow up in the narrow region between inclusions. The gradient of solutions depend on $ε$, the distance between the inclusions, where $ε$ approaches to $0$. By using the maximum principle techniques, we give another proof of the Dong-Li-Yang estimates \cite{DLY} for any convex inclusions of arbitrary shape with $n\geq 3$. This result solves the problem raised by \cite{W}, where the spherical inclusions with $n\geq 4$ is considered. Moreover, we also generalize the above results with flatter boundaries near touching points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_12089 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal gradient estimates for the insulated conductivity problem with dimensions more than two Ma, Linjie Analysis of PDEs In high-contrast composite materials, the electric (or stress) field may blow up in the narrow region between inclusions. The gradient of solutions depend on $ε$, the distance between the inclusions, where $ε$ approaches to $0$. By using the maximum principle techniques, we give another proof of the Dong-Li-Yang estimates \cite{DLY} for any convex inclusions of arbitrary shape with $n\geq 3$. This result solves the problem raised by \cite{W}, where the spherical inclusions with $n\geq 4$ is considered. Moreover, we also generalize the above results with flatter boundaries near touching points. |
| title | Optimal gradient estimates for the insulated conductivity problem with dimensions more than two |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2202.12089 |