共查询到10条相似文献,搜索用时 15 毫秒
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
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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
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Fethi BEN BELGACEM 《数学物理学报(B辑英文版)》2018,38(4):1285-1295
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
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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
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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
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Mihai P? AUN 《数学年刊B辑(英文版)》2008,29(6):623-630
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.
Mihai PAUN Institut lie Cartan Université Henri Poincaré Nancy BP Vandoeuvre-lès-Nancy Cedex France. 《数学年刊B辑(英文版)》2008,(6)
The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact Khler manifolds. 相似文献
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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