Applications of Interpolation theory to the regularity of some equasilinear PDEs
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908114439110656 |
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| author | Ahmed, Irshaad Fiorenza, Alberto Formica, Maria Rosaria Gogatishvili, Amiran Hamidi, Abdallah El |
| author_facet | Ahmed, Irshaad Fiorenza, Alberto Formica, Maria Rosaria Gogatishvili, Amiran Hamidi, Abdallah El |
| contents | We present some regularity results on the gradient of the weak or entropic-renormalized solution $u$ to the homogeneous Dirichlet problem for the quasilinear equations of the form
\begin{equation*}\label{p-laplacian_eq}
-{\rm div~}(|\nabla u|^{p-2}\nabla u)+V(x;u)=f,
\end{equation*} where $Ω$ is a bounded smooth domain of $\mathbb R^n$, $V$ is a nonlinear potential and $f$ belongs to non-standard spaces like Lorentz-Zygmund spaces.
Moreover, we collect some well-known and new results for identifying some interpolation spaces and enrich some contents with details. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications of Interpolation theory to the regularity of some equasilinear PDEs Ahmed, Irshaad Fiorenza, Alberto Formica, Maria Rosaria Gogatishvili, Amiran Hamidi, Abdallah El Analysis of PDEs Functional Analysis 46M35, 35J62, 35B45, 35D30, 35J25, 46E30, 46B70 We present some regularity results on the gradient of the weak or entropic-renormalized solution $u$ to the homogeneous Dirichlet problem for the quasilinear equations of the form \begin{equation*}\label{p-laplacian_eq} -{\rm div~}(|\nabla u|^{p-2}\nabla u)+V(x;u)=f, \end{equation*} where $Ω$ is a bounded smooth domain of $\mathbb R^n$, $V$ is a nonlinear potential and $f$ belongs to non-standard spaces like Lorentz-Zygmund spaces. Moreover, we collect some well-known and new results for identifying some interpolation spaces and enrich some contents with details. |
| title | Applications of Interpolation theory to the regularity of some equasilinear PDEs |
| topic | Analysis of PDEs Functional Analysis 46M35, 35J62, 35B45, 35D30, 35J25, 46E30, 46B70 |
| url | https://arxiv.org/abs/2411.00367 |