系数的L1相互关系对非线性退化椭圆方程解的正则性的影响

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1405-1414.

系数的L¹相互关系对非线性退化椭圆方程解的正则性的影响

邹维林*(),任远春(),肖美萍()

^{南昌航空大学数学与信息科学学院南昌 330063}

收稿日期:2020-07-16 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 邹维林 E-mail:zwl267@163.com;320029374@qq.com;59653147@qq.com
作者简介:任远春, E-mail: 320029374@qq.com|肖美萍, E-mail: 59653147@qq.com
基金资助:
国家自然科学基金(11801259);国家自然科学基金(11461048);江西省自然科学基金(20202BABL201009);江西省教育厅科技项目(GJJ170604)

Regularizing Effect of L¹ Interplay Between Coefficients in Nonlinear Degenerate Elliptic Equations

Weilin Zou*(),Yuanchun Ren(),Meipin Xiao()

^{College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063}

Received:2020-07-16 Online:2021-10-26 Published:2021-10-08
Contact: Weilin Zou E-mail:zwl267@163.com;320029374@qq.com;59653147@qq.com
Supported by:
the NSFC(11801259);the NSFC(11461048);the NSF of Jiangxi Province(20202BABL201009);the Education Department of Jiangxi Province(GJJ170604)

摘要/Abstract

摘要：

该文主要研究一类非线性退化椭圆型方程$-\mbox{div}（a（x，u，\nabla u））+b（x）g（u）+B（x，u，\nabla u）=f（x）$，其中方程的主算子在$\{u=0\}$处退化.即使当$f$仅属于$L^1$时，证明了有界弱解的存在性，这在某种程度上推广了以往的结果.

关键词: 退化椭圆型方程, L¹系数, 有界弱解, 正则性影响

Abstract:

In this paper, we consider a class of nonlinear degenerate elliptic equations of the form $-\mbox{div}(a(x,u,\nabla u))+b(x)g(u)+B(x,u,\nabla u)=f(x)$, where the principal part degenerates on $\{u=0\}$. Even if $f$ only belongs to $L^{1}(\Omega)$, the existence of bounded weak solutions are proven. This generalizes, to some extent, previous results.

Key words: Degenerate elliptic equations, L¹ coefficients, Bounded weak solutions, Regularizing effect

中图分类号:

O175.2

邹维林,任远春,肖美萍. 系数的L¹相互关系对非线性退化椭圆方程解的正则性的影响[J]. 数学物理学报, 2021, 41(5): 1405-1414.

Weilin Zou,Yuanchun Ren,Meipin Xiao. Regularizing Effect of L¹ Interplay Between Coefficients in Nonlinear Degenerate Elliptic Equations[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1405-1414.

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系数的L¹相互关系对非线性退化椭圆方程解的正则性的影响

Regularizing Effect of L¹ Interplay Between Coefficients in Nonlinear Degenerate Elliptic Equations

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