论文标题
$（p，a）$ - laplacian型椭圆方程的积极liouville定理和渐近行为，在莫雷空间中具有紫红色的潜力
Positive Liouville theorem and asymptotic behaviour for $(p,A)$-Laplacian type elliptic equations with Fuchsian potentials in Morrey space
论文作者
论文摘要
我们研究了liouville型定理和在\partialΩ\ cup \ cup \ {\ infty \} $ in quasilIrineareareareareareareareareareareareareareareareare type tyuness $ point $ζ\ {\ infty \} $附近的渐近行为u）+v | u |^{p-2} u = 0 \ quad \ text {in}ω\ setMinus \ {ζ\}，$$ 其中$ω$是$ \ mathbb {r}^d $（$ d \ geq 2 $）中的一个域，而$ a =（a_ {ij}）\ in l _ {\ rm loc}^{\ rm loc}^{\ infty} {\ infty}（ω; \; \ \ \ m}潜在的$ v $在于某个当地的莫雷领域（取决于$ p $），并且在$ζ$上具有紫红色型孤立的奇异性。
We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point $ζ\in\partialΩ\cup\{\infty\}$ of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } Ω\setminus\{ζ\},$$ where $Ω$ is a domain in $\mathbb{R}^d$ ($d\geq 2$), and $A=(a_{ij})\in L_{\rm loc}^{\infty}(Ω;\mathbb{R}^{d\times d})$ is a symmetric and locally uniformly positive definite matrix. The potential $V$ lies in a certain local Morrey space (depending on $p$) and has a Fuchsian-type isolated singularity at $ζ$.
