Gradient Hölder regularity in mixed local and nonlocal linear parabolic problem
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910297277595648 |
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| author | Das, Stuti |
| author_facet | Das, Stuti |
| contents | We prove the local Hölder regularity of weak solutions to the mixed local nonlocal parabolic equation of the form \begin{equation*} u_t-Δu+\text{P.V.}\int_{\mathbb{R}^{n}} {\frac{u(x,t)-u(y,t)}{{\left|x-y\right|}^{n+2s}}}dy=0, \end{equation*} where $0<s<1$; for every exponent $α_0\in(0,1)$. Here, $Δ$ is the usual Laplace operator. Next, we show that the gradients of weak solutions are also $α$-Hölder continuous for some $α\in (0,1)$. Our approach is purely analytic and it is based on perturbation techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07021 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gradient Hölder regularity in mixed local and nonlocal linear parabolic problem Das, Stuti Analysis of PDEs We prove the local Hölder regularity of weak solutions to the mixed local nonlocal parabolic equation of the form \begin{equation*} u_t-Δu+\text{P.V.}\int_{\mathbb{R}^{n}} {\frac{u(x,t)-u(y,t)}{{\left|x-y\right|}^{n+2s}}}dy=0, \end{equation*} where $0<s<1$; for every exponent $α_0\in(0,1)$. Here, $Δ$ is the usual Laplace operator. Next, we show that the gradients of weak solutions are also $α$-Hölder continuous for some $α\in (0,1)$. Our approach is purely analytic and it is based on perturbation techniques. |
| title | Gradient Hölder regularity in mixed local and nonlocal linear parabolic problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2306.07021 |