广西民族大学学报（自然科学版）2025，Vol.31Issue(1)：85-90,6.
变分法与对称极大曲面方程
Calculus of Variations and Symmetric Maximal Surface Equation
摘要
Abstract
By Calculus of Variations,this paper studies the existence of weak solutions of Dirichlet problem for the symmetric maximal surface equation{Qu=div(uDu/√1-|Du|2)+√1-|Du|2=0,in Ωu=φ,on ∂Ωin Lorentz-Minkowski space.The operator Q is variational and corresponds to the Euler-Lagrange operator of the energy functional I(·)of the variational problem I(u):=∫Ω u√1-|Du|2dx,in Ω u=φ,on ∂Ω,where u∈℘φ(Ω):={w∈C0,1(-Ω):w is strictly spacelike in Ω,w=φ on ∂Ω},φ∈C0,1(-Ω)is the given function.By first variation,the sufficient condition for the existence of weak solutions to the Dirichlet problem is that the variational problem admits maximizers.关键词
变分法/闵可夫斯基空间/对称极大曲面方程/类空Key words
Calculus of Variations/Minkowski space/Symmetric maximal surface equation/Spacelike分类
数学引用本文复制引用
吕家如,黄荣里..变分法与对称极大曲面方程[J].广西民族大学学报（自然科学版）,2025,31(1):85-90,6.基金项目
国家自然科学基金项目(11771103). （11771103）
