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- W2506877683 abstract "In this paper, we investigate solutions of the hyperbolic Poisson equation $Delta_{h}u(x)=psi(x)$, where $psiin L^{infty}(mathbb{B}^{n}, mathbb{R}^n)$ and [ Delta_{h}u(x)= (1-|x|^2)^2Delta u(x)+2(n-2)(1-|x|^2)sum_{i=1}^{n} x_{i} frac{partial u}{partial x_{i}}(x) ] is the hyperbolic Laplace operator in the $n$-dimensional space $mathbb{R}^n$ for $nge 2$. We show that if $ngeq 3$ and $uin C^{2}(mathbb{B}^{n},mathbb{R}^n) cap C(overline{mathbb{B}^{n}},mathbb{R}^n )$ is a solution to the hyperbolic Poisson equation, then it has the representation $u=P_{h}[phi]-G_{ h}[psi]$ provided that $umid_{mathbb{S}^{n-1}}=phi$ and $int_{mathbb{B}^{n}}(1-|x|^{2})^{n-1} |psi(x)|,dtau(x)<infty$. Here $P_{h}$ and $G_{h}$ denote Poisson and Green integrals with respect to $Delta_{h}$, respectively. Furthermore, we prove that functions of the form $u=P_{h}[phi]-G_{h}[psi]$ are bi-Lipschitz continuous." @default.
- W2506877683 created "2016-08-23" @default.
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- W2506877683 date "2016-07-19" @default.
- W2506877683 modified "2023-09-27" @default.
- W2506877683 title "On bi-Lipschitz continuity of solutions of hyperbolic Poisson's equation" @default.
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