| 任长宇,关晋瑞,袁洪君.一类一般形式的抛物型Monge-Ampbre方程[J].数学年刊A辑,2009,30(3):421~432 |
| 一类一般形式的抛物型Monge-Ampbre方程 |
| A Class of General Form Parabolic Monge-Ampēre Equation |
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| DOI： |
| 中文关键词: 一般形式 完全非线性 Monge-Ampére方程 |
| 英文关键词:General form, Fully nonlinear, Monge-Amp`ere equation |
| 基金项目:国家自然科学基金(No.J0630104)资助的项目 |
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| 中文摘要: |
| 对于Caffarelli-Nirenberg-Spruck提出的一种更一般形式的椭圆型Monge-AmpéFe算子det(D2u+σ),讨论与之对应的～种抛物型Monge-Ampére方程第一初边值同题.在一定的结构性条件下,利用连续性方法证明了其古典解的存在惟-性. |
| 英文摘要: |
| For a class of general elliptic Monge-Amp`ere operators det(D2u + ) which
raised by Caffarelli-Nirenberg-Spruck, the corresponding parabolic Monge-Amp`ere equation
is studied. Under some structural assumptions, the existence and uniqueness of the classical
solution to the first boundary-initial value problem for the equation are established by means
of a continuation approach. |
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