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.
出处
《应用数学》
CSCD
北大核心
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)
