Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class

Giri Ratan Kr.; Pinchover Yehuda

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Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class

机译：Wolff类中具有Fuchsian势的准线性椭圆方程的正解

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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 zeta is an element of delta Omega U {infinity} for the quasilinear elliptic equation -div(del u(p-2)(A) A del u) + V u(p-2)u = 0 in Omega, where Omega is a domain in R-d, d >= 2, 1 < p < d, and A = (a(ij)) is an element of L-loc(infinity)(Omega; R-dxd) 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 zeta is an element of delta Omega U {infinity}.

机译：使用 Harnack 不等式和标度论证，我们研究了 Liouville 型定理和孤立奇异点附近正解的渐近行为 zeta 是 delta Omega U {infinity} 的一个元素，用于准线性椭圆方程 -div（|del u|（p-2）（A） A del u） + V |u|（p-2）u = 0 在 Omega 中，其中 Omega 是 R-d 中的一个域，d >= 2， 1 < p < d，A = （a（ij））是 L-loc（infinity）（Omega;R-dxd）是一个对称且局部均匀的正定矩阵。假设势 V 属于某个 Wolff 类，并且在孤立点处具有广义 Fuchsian 型奇点 zeta 是 delta Omega U {infinity} 的一个元素。

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来源
《Milan Journal of Mathematics》 |2023年第1期|59-96|共38页
作者
Giri Ratan Kr.; Pinchover Yehuda;
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作者单位

Technion Israel Inst Technol;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
Fuchsian singularity; Morrey spaces; Kato class; Wolff class; Liouville theorem; Quasilinear elliptic equation; (p; A)-Laplacian; KATO CLASS POTENTIALS; HARNACK INEQUALITY; P-LAPLACIAN; ISOLATED SINGULARITIES; SCHRODINGER-OPERATORS;

机译：紫红色奇点;莫里空间;加藤类;沃尔夫类;Liouville定理;准线性椭圆方程;（p;A）-拉普拉斯;加藤级潜力;哈纳克不等式;P-拉普拉斯;孤立奇点;薛定谔-运营商;

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Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class

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