论文标题
沃尔夫类中具有紫红色电位的准椭圆方程的阳性解
Positive solutions of quasilinear elliptic equations with Fuchsian potentials in Wolff class
论文作者
论文摘要
利用Harnack的不平等和扩展论点，我们研究了Liouville-type定理以及在\partialω\ cup \ cup \ cup \ cup \ {\ infty \} $ in \pottialΩ u | _a^{p-2} a \ nabla u）+v | u |^{p-2} u = 0 \ quad \ text \ text {in}Ω l _ {\ rm loc}^{\ infty}（ω; \ mathbb {r}^{d \ times d}）$是一种对称且本地均匀的确定矩阵。假定潜在的$ v $属于某个沃尔夫类，并且在一个孤立的点$ζ\ in \partialΩ\ cup \ cup \ {\ infty \} $上具有广义的fuchsian型奇异性。
Using Harnack's inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point $ζ\in \partialΩ\cup\{\infty\}$ for the quasilinear elliptic equation $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{ in } Ω,$$ where $Ω$ is a domain in $\mathbb{R}^d$, $d\geq 2$, $1<p<d$, and $A=(a_{ij})\in L_{\rm loc}^{\infty}(Ω; \mathbb{R}^{d\times d})$ is a symmetric and locally uniformly positive definite matrix. It is assumed that the potential $V$ belongs to a certain Wolff class and has a generalized Fuchsian-type singularity at an isolated point $ζ\in \partial Ω\cup \{\infty\}$.
