Gradient and Hessian regularity in elliptic transmission problems near a point cusp
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910402695135232 |
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| author | Bothe, Dieter Druet, Pierre-Etienne Haller, Robert |
| author_facet | Bothe, Dieter Druet, Pierre-Etienne Haller, Robert |
| contents | We consider elliptic transmission problems in several space dimensions near an interface which is $C^{1,1}$ diffeomorphic to an axisymmetric reference-interface with a singular point of cusp type. We establish the regularity of the gradient and of the Hessian in $L^p$ spaces up to the cusp point for local weak solutions. We obtain regularity thresholds which are different according to whether the cusp is inward or outward to the subdomain, and which depend explicitly on the opening of the interface at the cusp. Our results allow for source terms in the bulk and on the interface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient and Hessian regularity in elliptic transmission problems near a point cusp Bothe, Dieter Druet, Pierre-Etienne Haller, Robert Analysis of PDEs 35A21, 35B45, 35B65, 35D35, 35J15, 35R05 We consider elliptic transmission problems in several space dimensions near an interface which is $C^{1,1}$ diffeomorphic to an axisymmetric reference-interface with a singular point of cusp type. We establish the regularity of the gradient and of the Hessian in $L^p$ spaces up to the cusp point for local weak solutions. We obtain regularity thresholds which are different according to whether the cusp is inward or outward to the subdomain, and which depend explicitly on the opening of the interface at the cusp. Our results allow for source terms in the bulk and on the interface. |
| title | Gradient and Hessian regularity in elliptic transmission problems near a point cusp |
| topic | Analysis of PDEs 35A21, 35B45, 35B65, 35D35, 35J15, 35R05 |
| url | https://arxiv.org/abs/2404.05827 |