Global higher integrability for systems with $p$-growth structure in noncylindrical domains
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914135695949824 |
|---|---|
| author | Moring, Kristian Scheven, Christoph Schätzler, Leah |
| author_facet | Moring, Kristian Scheven, Christoph Schätzler, Leah |
| contents | We consider the Cauchy-Dirichlet problem to systems with $p$-growth structure with $1 < p < \infty$, whose prototype is \begin{equation*}
\partial_t u- \operatorname{div} \big( |Du|^{p-2} Du \big) = \operatorname{div} \left( |F|^{p-2} F \right), \end{equation*} in a bounded noncylindrical domain $E \subset \mathbb{R}^{n+1}$. For $p> \frac{2(n+1)}{n+2}$ and domains $E$ that satisfy suitable regularity assumptions and do not grow or shrink too fast, we prove global higher integrability of $Du$. The result is already new in the case $p=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global higher integrability for systems with $p$-growth structure in noncylindrical domains Moring, Kristian Scheven, Christoph Schätzler, Leah Analysis of PDEs 35B65, 35K51, 35K55, 35R37 We consider the Cauchy-Dirichlet problem to systems with $p$-growth structure with $1 < p < \infty$, whose prototype is \begin{equation*} \partial_t u- \operatorname{div} \big( |Du|^{p-2} Du \big) = \operatorname{div} \left( |F|^{p-2} F \right), \end{equation*} in a bounded noncylindrical domain $E \subset \mathbb{R}^{n+1}$. For $p> \frac{2(n+1)}{n+2}$ and domains $E$ that satisfy suitable regularity assumptions and do not grow or shrink too fast, we prove global higher integrability of $Du$. The result is already new in the case $p=2$. |
| title | Global higher integrability for systems with $p$-growth structure in noncylindrical domains |
| topic | Analysis of PDEs 35B65, 35K51, 35K55, 35R37 |
| url | https://arxiv.org/abs/2511.02553 |