Global boundedness of solutions of degenerate and non-uniform parabolic equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912611422961664 |
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| author | Dang, Thuyen Duc, Duong Minh |
| author_facet | Dang, Thuyen Duc, Duong Minh |
| contents | Let $2 \le N\in\mathbb{N}$, $Ω$ be a bounded open in $\mathbb{R}^{N}$, $T\in (0,\infty)$, $Q=Ω\times (0,T)$, $u$ be a weak solution of parabolic equation $\displaystyle \frac{\partial u}{\partial t} -Lu= f$, where $L$ is an elliptic operator on a space of functions on $Q$. The coefficients of $L$ may not be bounded, not strictly nor uniformly elliptic, and not of Muckenhoupt type. We obtain global boundedness of $u$. Our result can be applied to $u$, which may vanish on $(A\times (0,T))\cup (Ω\times \{0\})$ of the boundary of $Q$ and is free outside this set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global boundedness of solutions of degenerate and non-uniform parabolic equations Dang, Thuyen Duc, Duong Minh Analysis of PDEs 26D10, 35J70, 35J75, 35J08, 35J15 Let $2 \le N\in\mathbb{N}$, $Ω$ be a bounded open in $\mathbb{R}^{N}$, $T\in (0,\infty)$, $Q=Ω\times (0,T)$, $u$ be a weak solution of parabolic equation $\displaystyle \frac{\partial u}{\partial t} -Lu= f$, where $L$ is an elliptic operator on a space of functions on $Q$. The coefficients of $L$ may not be bounded, not strictly nor uniformly elliptic, and not of Muckenhoupt type. We obtain global boundedness of $u$. Our result can be applied to $u$, which may vanish on $(A\times (0,T))\cup (Ω\times \{0\})$ of the boundary of $Q$ and is free outside this set. |
| title | Global boundedness of solutions of degenerate and non-uniform parabolic equations |
| topic | Analysis of PDEs 26D10, 35J70, 35J75, 35J08, 35J15 |
| url | https://arxiv.org/abs/2509.23064 |