Weak comparison principle for widely degenerate elliptic equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866909662441373696 |
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| author | Grimaldi, Antonio Giuseppe Russo, Stefania |
| author_facet | Grimaldi, Antonio Giuseppe Russo, Stefania |
| contents | We prove a comparison principle for local weak solutions to a class of widely degenerate elliptic equations of the form \begin{equation}
-\text{div} \left( \left(|Du|-1 \right)^{p-1}_+\frac{Du}{|Du|} \right) = f(x,u) \qquad \text{ in } Ω,\notag
\end{equation}
where $p \ge 2$ and $Ω$ is an open subset of $\mathbb{R}^{n}$, $n\geq2$.
Moreover, we establish some second order regularity results of the solutions, that yields a weighted Sobolev inequality with widely degenerate weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak comparison principle for widely degenerate elliptic equations Grimaldi, Antonio Giuseppe Russo, Stefania Analysis of PDEs We prove a comparison principle for local weak solutions to a class of widely degenerate elliptic equations of the form \begin{equation} -\text{div} \left( \left(|Du|-1 \right)^{p-1}_+\frac{Du}{|Du|} \right) = f(x,u) \qquad \text{ in } Ω,\notag \end{equation} where $p \ge 2$ and $Ω$ is an open subset of $\mathbb{R}^{n}$, $n\geq2$. Moreover, we establish some second order regularity results of the solutions, that yields a weighted Sobolev inequality with widely degenerate weights. |
| title | Weak comparison principle for widely degenerate elliptic equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.22128 |