吉林大学学报（理学版）2025，Vol.63Issue(3)：685-690,6.DOI:10.13413/j.cnki.jdxblxb.2024329
一类具低阶项的拟线性椭圆方程弱解的存在性
Existence of Weak Solutions to a Class of Quasi-linear Elliptic Equations with Lower Order Terms
摘要
Abstract
By using the weak convergence methods for nonlinear partial differential equations(PDEs),the author proved the existence of solutions to a class of quasi-linear elliptic equations with gradient term and zero-order term.The main characteristic of the equation was that the coefficient function of the gradient term b∈LN(Ω),but its norm‖b‖N,Ω was not required to be sufficiently small.Firstly,by segmenting the bounded domain Ω,the solution sequence {u∈}0＜∈＜1 was split into a sum of some subfunctions,and the energy estimate of the subfunction was limited to small subdomain.Secondly,the author obtained the energy estimate of {u∈}0＜∈＜1 on W1,90(Ω)by using iterative techniques.Finally,with the help of Boccardo-Murat's technique,the author proved the almost everywhere convergence of the gradient solution sequence {▽u∈}0＜,＜1,and determined the convergence element of the nonlinear term of the equation based on this convergence.关键词
椭圆方程/拟线性/低阶项Key words
elliptic equation/quasi-linear/lower order term分类
数理科学引用本文复制引用
李仲庆..一类具低阶项的拟线性椭圆方程弱解的存在性[J].吉林大学学报（理学版）,2025,63(3):685-690,6.基金项目
国家自然科学基金青年科学基金(批准号:11901131). （批准号:11901131）
