Embeddings of anisotropic Sobolev spaces into spaces of anisotropic Hölder-continuous functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915027198410752 |
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| author | Eddine, Nabil Chems Repovš, Dušan D. |
| author_facet | Eddine, Nabil Chems Repovš, Dušan D. |
| contents | We introduce a novel framework for embedding anisotropic variable exponent Sobolev spaces into spaces of anisotropic variable exponent Hölder-continuous functions within rectangular domains. We establish a foundational approach to extend the concept of Hölder continuity to anisotropic settings with variable exponents, providing deeper insight into the regularity of functions across different directions. Our results not only broaden the understanding of anisotropic function spaces but also open new avenues for applications in mathematical and applied sciences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embeddings of anisotropic Sobolev spaces into spaces of anisotropic Hölder-continuous functions Eddine, Nabil Chems Repovš, Dušan D. Functional Analysis Analysis of PDEs 46E35, 46E15 We introduce a novel framework for embedding anisotropic variable exponent Sobolev spaces into spaces of anisotropic variable exponent Hölder-continuous functions within rectangular domains. We establish a foundational approach to extend the concept of Hölder continuity to anisotropic settings with variable exponents, providing deeper insight into the regularity of functions across different directions. Our results not only broaden the understanding of anisotropic function spaces but also open new avenues for applications in mathematical and applied sciences. |
| title | Embeddings of anisotropic Sobolev spaces into spaces of anisotropic Hölder-continuous functions |
| topic | Functional Analysis Analysis of PDEs 46E35, 46E15 |
| url | https://arxiv.org/abs/2411.08829 |