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1.
In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with H?lder-continuous ?rst derivatives of exponent β 1/5. Our approach is based on combining the approach of Lewicka and Pakzad(2017) with a new diagonalization procedure which avoids the use of conformal coordinates, which was introduced by De Lellis et al.(2018) for the isometric immersion problem.  相似文献   

2.
By means of the classical symmetry method,a hyperbolic Monge-Ampère equation is investigated.The symmetry group is studied and its corresponding group invariant solutions are constructed.Based on the associated vector of the obtained symmetry,the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation,from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully.  相似文献   

3.
In this paper, we introduce and study a method for the numerical solution of the elliptic Monge-Ampère equation with Dirichlet boundary conditions. We formulate the Monge-Ampère equation as an optimization problem. The latter involves a Poisson Problem which is solved by the finite element Galerkin method and the minimum is computed by the conjugate gradient algorithm. We also present some numerical experiments.  相似文献   

4.
本文考虑了四元数空间Hn中齐次四元Monge-Ampère方程的狄利克雷问题解的正则性.首先,当区域是边界为C1,1的强拟凸域时,作者给出了解的Lipschitz估计.其次,考虑了四元MongeAmpère算子的收敛性.最后,讨论了齐次四元Monge-Ampère方程的粘性次解与F-次调和函数之间的关系.  相似文献   

5.
向妮  吴燕  窦楠  张俊玮 《数学杂志》2017,37(6):1261-1274
本文研究了一类抛物型Monge-Ampère型方程的Cauchy-Neumann问题.通过构造辅助函数,利用函数在极大值点的性质及柯西不等式等方法对方程的解进行估计,得到了方程解的全局二阶梯度估计.接着利用抛物方程的一般理论,进一步得到在光滑条件下,解的长时间存在性,推广了抛物型Monge-Ampère方程的结果.  相似文献   

6.
任长宇  王光烈 《东北数学》2007,23(5):413-424
This paper deals with a class of parabolic Monge-Ampère equation on Riemannian manifolds. The existence and uniqueness of the solution to the first initial-boundary value problem for the equation are established.  相似文献   

7.
The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact Kǎhler manifolds.  相似文献   

8.
The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact Khler manifolds.  相似文献   

9.
过去50年间,复Monge-Ampère方程是一个被广泛研究的主题,它在复分析、复几何和K?hler几何中有很多重要的应用.本文首先回顾一些经典结果,然后着重介绍关于复Monge-Ampère方程的Liouville定理、C~(1,α)估计和C~(2,α)估计,以及其在Sasakian几何中的一些应用.这些结果是与S.Dinew、管鹏飞、李超、李嘉禹和张享文等合作得到的.  相似文献   

10.
By means of the classical symmetry method,a hyperbolic Monge-Ampère equation is investigated.The symmetry group is studied and its corresponding group invariant solutions are constructed.Based on the a...  相似文献   

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