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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18830 |
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| _version_ | 1866914888835661824 |
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| author | De Luca, Alessandra |
| author_facet | De Luca, Alessandra |
| contents | The present paper aims at representing an improvement of the result in [2], where a strong unique continuation property and a description of the local behaviour around the edge of a crack for solutions to an elliptic problem are established, by relaxing the star-shapedness condition on the complement of the crack. More specifically, this assumption will be dropped off by applying a suitable diffeomorphism which straightens the boundary of the crack, before performing the approximation procedure developed in [2] in order to derive a suitable monotonicity formula. This will yield the appearence of a matrix in the equation, which shall be handled appropriately: for this we will take a hint from [4]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on geometric assumptions for unique continuation from the edge of a crack De Luca, Alessandra Analysis of PDEs The present paper aims at representing an improvement of the result in [2], where a strong unique continuation property and a description of the local behaviour around the edge of a crack for solutions to an elliptic problem are established, by relaxing the star-shapedness condition on the complement of the crack. More specifically, this assumption will be dropped off by applying a suitable diffeomorphism which straightens the boundary of the crack, before performing the approximation procedure developed in [2] in order to derive a suitable monotonicity formula. This will yield the appearence of a matrix in the equation, which shall be handled appropriately: for this we will take a hint from [4]. |
| title | A note on geometric assumptions for unique continuation from the edge of a crack |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.18830 |