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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12609 |
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| _version_ | 1866917209563987968 |
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| author | Corella, Alberto Domínguez Rivera-Noriega, Jorge |
| author_facet | Corella, Alberto Domínguez Rivera-Noriega, Jorge |
| contents | We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boundary of this class of domains is a mixed Lipschitz condition, as described in the bulk of the paper. The main tool is an adequate version of the implicit function theorem for functions with this kind of regularity. It is proved that the class introduced herein is of the same type as domains previously considered by several authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12609 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A class of non-cylindrical domains for parabolic equations Corella, Alberto Domínguez Rivera-Noriega, Jorge Analysis of PDEs We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boundary of this class of domains is a mixed Lipschitz condition, as described in the bulk of the paper. The main tool is an adequate version of the implicit function theorem for functions with this kind of regularity. It is proved that the class introduced herein is of the same type as domains previously considered by several authors. |
| title | A class of non-cylindrical domains for parabolic equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.12609 |