Lax-Milgram定理的一个推广及其应用  

A Generalization and Application of Lax-Milgram Theorem

作　　者：张馨予 吕颖[2] ZHANG Xin-yu;LYU Ying(School of Mathematics, Sichuan University, Chengdu 610064, China;School of Mathematics and statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]四川大学数学学院,成都610064 [2]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2020年第6期29-32,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11601438)。

摘　　要：把经典的Lax-Milgram定理中的双线性条件推广到仅对某一个变量线性,在适当的弱下半连续强制条件下,证明了变分泛函l(x)=1/pa(x,x)-b(x)存在唯一解,并将其应用于研究p-Laplace算子边值问题解的存在唯一性.In this paper,the bilinear functional condition required in the classical Lax-Milgram theorem has been generalized to be linear with only one argument.Under the appropriate weak lower semi-continuous constraint,we prove that the variational functional l(x)=1/pa(x,x)-b(x)has a unique solution and apply it to the existence and uniqueness of the solutions of the p-Laplace boundary value problem.

关 键 词：Fréchet-Riesz表现定理 Lax-Milgram定理 弱下半连续 强制性 P-LAPLACE算子 

分 类 号：O177.1[理学—数学]