【摘要】 对于Caffarelli-Nirenberg-Spruck提出的一种更一般形式的椭圆型Monge-Ampère算子det(D~2u+σ),讨论与之对应的一种抛物型Monge-Ampère方程第一初边值问题。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一性。更多还原

【Abstract】 For a class of general elliptic Monge-Ampère operators det(D~2u+σ) which raised by Caffarelli-Nirenberg-Spruck,the corresponding parabolic Monge-Ampère 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.更多还原