一类P-Laplace型椭圆方程组非常弱解的存在性  

Existence of very weak solutions for a class of P-Laplacian elliptic equations

作　　者：陈淑红 郭磊 CHEN Shuhong;GUO Lei(School of Mathematics and Computer,Wuyi University,Wuyishan 354300,China)

机构地区：[1]武夷学院数学与计算机学院,福建武夷山354300

出　　处：《广西大学学报（自然科学版）》2023年第1期236-245,共10页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金项目(11571159);武夷学院引进人才科研启动项目(YJ202118);福建省自然科学基金项目(2021J011144)。

摘　　要：为了建立非齐次项是P-Laplace型算子的椭圆方程组非常弱解的存在性,构造适当的相对截断函数作为检验函数,并通过适当形式的权函数,结合相对覆盖分解和权重、散度-旋度定理等偏微分方程证明技巧,得到了具有P-Laplace型椭圆方程组非常弱解的存在性。In order to establish the existence of very weak solutions for elliptic equations whose in-homogeneous terms are P-Laplace operators,the appropriate relative truncation function was constructed as the test function in the definition of very weak solution.Then through the appropriate form of weight function,combining the relative covering decomposition with partial differential equation proof techniques such as weight and divergence-curl theorem,the desired results of the very weak solutions existence theory for elliptic systems with P-Laplace operator were obtained.

关 键 词：P-Laplace型算子 椭圆方程 非常弱解 存在性 

分 类 号：O175.2[理学—数学]