一类Curvature方程的两种边值问题解的存在性  

Existence of Solutions of One Kind Curvature Equation with Two Kinds of Boundary Value Conditions

作　　者：魏利[1] 谭瑞林[1] 樊树新 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《应用数学》2014年第1期131-139,共9页Mathematica Applicata

基　　金：国家自然科学基金项目(11071053);河北省自然科学基金项目(A2010001482);河北省教育厅科学研究重点项目资助课题(ZH2012080);河北经贸大学科学研究重点项目(2013KYZ01)

摘　　要：利用含有伪单调算子的变分不等式解的存在性定理,证明一类具有Dirichlet边值条件的Curvature方程在W1,p(Ω)空间中存在唯一解.深入研究具有Dirichlet边值条件的Curvature方程和具有Neumann边值条件的Curvature方程之间的关系,利用极大单调算子值域的扰动理论,给出具有Neumann边值条件的Curvature方程在W1,p(Ω)空间中存在解的充分条件.文中采用一些新的证明技巧,推广和补充了以往的相关研究成果.By using the result of the existence of solution of variational inequalities for pseudo-monotone operators, the existence and uniqueness of the curvature equation with Dirichlet boundary value conditions in W^1,p（Ω） is proved. By deeply researching the relation- ship between the curvature equation with Dirichlet boundary value conditions and the curvature equation with Neumann boundary value conditions and by using a perturbation result on the ranges for maximal monotone operators,a sufficient condition that the curvature equation with Neumann boundary value conditions has solutions in W^1,p（Ω） is proved. Some new techniques are employed in this paper, which extend or complement some corresponding results.

关 键 词：伪单调算子 极大单调算子 值域扰动 Curvature方程 Dirichlet边值 NEUMANN边值 

分 类 号：O177.91[理学—数学]