Regularity results for elliptic and parabolic systems of partial differential equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912172798377984 |
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| author | Angluli, Luciana Ferrari, Simone Lorenzi, Luca |
| author_facet | Angluli, Luciana Ferrari, Simone Lorenzi, Luca |
| contents | We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the space of bounded and continuous functions over $\R^d$. Consequently, we deduce relevant regularity results both in Hölder and Zygmund spaces and in Sobolev and Besov spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity results for elliptic and parabolic systems of partial differential equations Angluli, Luciana Ferrari, Simone Lorenzi, Luca Analysis of PDEs 35J47, 35K45, 47D06 We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the space of bounded and continuous functions over $\R^d$. Consequently, we deduce relevant regularity results both in Hölder and Zygmund spaces and in Sobolev and Besov spaces. |
| title | Regularity results for elliptic and parabolic systems of partial differential equations |
| topic | Analysis of PDEs 35J47, 35K45, 47D06 |
| url | https://arxiv.org/abs/2412.21014 |