Higher Hölder regularity for a subquadratic nonlocal parabolic equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914770522734592 |
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| author | Garain, Prashanta Lindgren, Erik Tavakoli, Alireza |
| author_facet | Garain, Prashanta Lindgren, Erik Tavakoli, Alireza |
| contents | In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation $$ \partial_t u+(-Δ_p)^s u = 0. $$ Here, $(-Δ_p)^s$ is the fractional $p$-Laplacian, $0<s<1$ and $1<p<2$. We establish Hölder regularity with explicit Hölder exponents. We also include the inhomogeneous equation with a bounded inhomogeneity. In some cases, the obtained Hölder exponents are almost sharp. Our results complement the previous results for the superquadratic case when $p\geq 2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_16640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Hölder regularity for a subquadratic nonlocal parabolic equation Garain, Prashanta Lindgren, Erik Tavakoli, Alireza Analysis of PDEs In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation $$ \partial_t u+(-Δ_p)^s u = 0. $$ Here, $(-Δ_p)^s$ is the fractional $p$-Laplacian, $0<s<1$ and $1<p<2$. We establish Hölder regularity with explicit Hölder exponents. We also include the inhomogeneous equation with a bounded inhomogeneity. In some cases, the obtained Hölder exponents are almost sharp. Our results complement the previous results for the superquadratic case when $p\geq 2$. |
| title | Higher Hölder regularity for a subquadratic nonlocal parabolic equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.16640 |