Removable singularities for quasilinear elliptic equations with source terms involving the solution and its gradient
Removable singularities for quasilinear elliptic equations with source terms involving the solution and its gradient
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源项涉及解及其梯度的拟线性椭圆方程的可去除奇点
DOI：
10.1007/s00574-022-00283-y
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kentaro Hirata
中科院分区：
文献类型：
--
作者：
Kentaro Hirata
本文建立了具有以下源项的拟线性椭圆型方程的可去性奇性定理：源项为：\Docentclass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setLong{oddsidemargin}{-69pt}\Begin{Document}$\Begin{Align}-\Delta_p u=a|u|^q+b|\具有非负有界Borel可测函数的nabla u|^S+c|^\u|^\sigma|\nabla u|^\tau\end$$\end{DOCUMENT}，B、取正数。特别地，当E是满足一致Minkowski条件的紧集时，我们给出了指数的上界和非负弱解推广到整个AS解的一个尖锐增长条件。
This paper establishes a removable singularity theorem for the quasilinear elliptic equations with source terms like \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\Delta _p u = a |u|^q + b|\nabla u|^s + c|u|^\sigma |\nabla u|^\tau \end{aligned}$$\end{document}with nonnegative bounded Borel measurable functionsa,b,cand positive numbers. In particular, we give upper bounds of exponentsand a sharp growth condition for nonnegative weak solutions into be extended to the whole ofas solutions, whenEis a compact set satisfying a uniform Minkowski condition.