Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates

IF 2.4 2区 数学 Q1 MATHEMATICS
Sun-Sig Byun , Minkyu Lim
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引用次数: 0

Abstract

We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak solution, where the right-hand side of the equation is the divergence of a vector-valued function with a low degree of integrability. To obtain this estimate, we adopt a notion of reverse Hölder class of Muckenhoupt weights. Another crucial part of the proof is a generalized weighted div-curl lemma in the setting of Orlicz spaces.
具有非标准增长和全局加权梯度估计的非线性椭圆方程极弱解的存在性
研究了一类具有非标准增长的拟线性椭圆型方程,证明了该类问题的一个极弱解的存在性。证明中的一个关键成分是一个非常弱解的先验全局加权梯度估计,其中方程的右侧是一个具有低可积度的向量值函数的散度。为了得到这个估计,我们采用了一个反向Hölder Muckenhoupt权重类的概念。证明的另一个关键部分是在Orlicz空间中一个广义加权div-旋度引理。
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
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