Remark on a special class of Finsler $p$-Laplacian equation
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| Format: | Preprint |
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2022
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| _version_ | 1866916293585666048 |
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| author | Li, Yuan Ye, Dong |
| author_facet | Li, Yuan Ye, Dong |
| contents | We investigate the anisotropic elliptic equation $-Δ_p^H u = g(u)$. Recently, Esposito, Riey, Sciunzi, and Vuono introduced an anisotropic Kelvin transform in their work \cite{ERSV2022} under the $(H_M)$ condition, where $H(ξ)=\sqrt{\langle Mξ,ξ\rangle}$ with a positive definite symmetric matrix $M$. Here, we emphasize that under the $(H_M)$ assumption, the Finsler $p$-Laplacian and the classical $p$-Laplacian operator are equivalent following a linear transformation. This equivalence offers us a more direct route to derive the pivotal findings presented in \cite{ERSV2022}. While this equivalence is crucial and noteworthy, to our knowledge, it has not been explicitly stated in the current literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_03439 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Remark on a special class of Finsler $p$-Laplacian equation Li, Yuan Ye, Dong Analysis of PDEs We investigate the anisotropic elliptic equation $-Δ_p^H u = g(u)$. Recently, Esposito, Riey, Sciunzi, and Vuono introduced an anisotropic Kelvin transform in their work \cite{ERSV2022} under the $(H_M)$ condition, where $H(ξ)=\sqrt{\langle Mξ,ξ\rangle}$ with a positive definite symmetric matrix $M$. Here, we emphasize that under the $(H_M)$ assumption, the Finsler $p$-Laplacian and the classical $p$-Laplacian operator are equivalent following a linear transformation. This equivalence offers us a more direct route to derive the pivotal findings presented in \cite{ERSV2022}. While this equivalence is crucial and noteworthy, to our knowledge, it has not been explicitly stated in the current literature. |
| title | Remark on a special class of Finsler $p$-Laplacian equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2208.03439 |