Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915483201044480 |
|---|---|
| author | Li, Qifan |
| author_facet | Li, Qifan |
| contents | We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is
\begin{equation*}\begin{split} \partial_t(|u|^{q-1}u)+\mathrm{P}.\mathrm{V}.\int_{\mathbb{R}^n}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+sp}}\,\mathrm{d}y=0, \end{split} \end{equation*} where $0<s<1$, $p>2$ and $0<q<p-1$. Under a parabolic tail condition, we show that any locally bounded and sign-changing solution is locally Hölder continuous. Our proof is based on a nonlocal version of De Giorgi technique and the method of intrinsic scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations Li, Qifan Analysis of PDEs We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is \begin{equation*}\begin{split} \partial_t(|u|^{q-1}u)+\mathrm{P}.\mathrm{V}.\int_{\mathbb{R}^n}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+sp}}\,\mathrm{d}y=0, \end{split} \end{equation*} where $0<s<1$, $p>2$ and $0<q<p-1$. Under a parabolic tail condition, we show that any locally bounded and sign-changing solution is locally Hölder continuous. Our proof is based on a nonlocal version of De Giorgi technique and the method of intrinsic scaling. |
| title | Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.05914 |