论文标题
关于特殊类的Finsler $ P $ -Laplacian方程的评论
Remark on a special class of Finsler $p$-Laplacian equation
论文作者
论文摘要
我们研究各向异性椭圆方程$-Δ_P^h u = g（u）$。最近，Esposito，Riey，Sciunzi和Vuono在$（H_M）$条件下的作品中引入了各向异性开尔文转换\ Cite {erSv2022}，其中$ h（ξ）= \ sqrt {\ sqrt {\ sqrt {\ langle mpect，nangle mpect，pottertime sysects $ sysercient contrice and sysectience y sysectience y sysectience y sysect n nique contrice。在这里，我们强调的是，在$（H_M）$假设下，Finsler $ P $ -Laplacian和经典的$ P $ -Laplacian操作员在线性转换之后相当。这种等价为我们提供了更直接的路线，以得出\ cite {erSv2022}中介绍的关键发现。据我们所知，尽管这种等价性至关重要且值得注意，但在当前文献中尚未明确说明。
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.
