首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we present a new method to compute the numerical solution of the elliptic Monge-Ampère equation. This method is based on solving a parabolic Monge-Ampère equation for the steady state solution. We study the problem of global existence, uniqueness, and convergence of the solution of the fully nonlinear parabolic PDE to the unique solution of the elliptic Monge-Ampère equation. Some numerical experiments are presented to show the convergence and the regularity of the numerical solution.  相似文献   

2.
Letz=z(x, y) be a real-valued twice continuously differentiable solution of the elliptic Monge-Ampère equationAr+2Bs+Ct+rt – s 2=E in the punctured disk 0<(x–x 0)2+(y–y 0)2<2. Assume thatq is continuous at (x0, y0). Our aim is to give sufficient conditions on the coefficientsA,..., E which ensure that the singularity (x 0,y 0) is removable. This generalizes an earlier result of Jörgens (Math. Ann. 129 (1955), 330–344).  相似文献   

3.
This paper presents a partial classification for C type-changing symplectic Monge-Ampère partial differential equations (PDEs) that possess an infinite set of first-order intermediate PDEs. The normal forms will be quasi-linear evolution equations whose types change from hyperbolic to either parabolic or to zero. The zero points can be viewed as analogous to singular points in ordinary differential equations. In some cases, intermediate PDEs can be used to establish existence of solutions for ill-posed initial value problems.  相似文献   

4.
Bo Guan  Qun Li 《Advances in Mathematics》2010,225(3):1185-2026
We study the Dirichlet problem for complex Monge-Ampère equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result (Theorem 1.1) extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in Cn. We also consider the equation on compact manifolds without boundary, attempting to generalize Yau's theorems in the Kähler case. As applications of the main result we study some connections between the homogeneous complex Monge-Ampère (HCMA) equation and totally real submanifolds, and a special Dirichlet problem for the HCMA equation related to Donaldson's conjecture on geodesics in the space of Kähler metrics.  相似文献   

5.
For a class of elliptic Hessian operators raised by Caffarelli-Nirenberg-Spruck, the corresponding parabolic Monge-Ampère equation was studied, the existence and uniqueness of the admissible solution to the first initial-boundary value problem for the equation were established, which extended a result of Ivochkina-Ladyzhenskaya.  相似文献   

6.
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   

7.
A contact distribution C on a manifold M determines a symplectic bundle CM. In this paper we find normal forms for its lagrangian distributions by classifying vector fields lying in C. Such vector fields are divided into three types and described in terms of the simplest ones (characteristic fields of 1st order PDE's). After having established the equivalence between parabolic Monge-Ampère equations (MAE's) and lagrangian distributions in terms of characteristics, as an application of our results we give normal forms for parabolic MAE's.  相似文献   

8.
Summary We consider real Monge-Ampère equations and we present two new properties of these equations. First, we show the existence of the «first eigenvalue of Monge-Ampère equation» i.e. we show the existence of a positive constant possessing all the properties of the first eigenvalue of a 2-nd order elliptic operator (positivity, uniqueness of the eigenfunction, maximum principle, bifurcation...).The second property concerns variational characterisations of solutions. Both properties are closely related to similar properties of the general class of Hamilton-Jacobi-Bellman equations.  相似文献   

9.
We give a simple proof of a result of Xinan Ma concerning a necessary condition for the solvability of the two-dimensional Monge-Ampère equation subject to the contact angle or capillarity boundary condition. Our technique works for more general Monge-Ampère equations in any dimension, and also extends to some other boundary conditions.

  相似文献   


10.
In dimension n?3, we define a generalization of the classical two-dimensional partial Legendre transform, that reduces interior regularity of the generalized Monge-Ampère equation to regularity of a divergence form quasilinear system of special form. This is then used to obtain smoothness of C2,1 solutions, having n-1 nonvanishing principal curvatures, to certain subelliptic Monge-Ampère equations in dimension n?3. A corollary is that if k?0 vanishes only at nondegenerate critical points, then a C2,1 convex solution u is smooth if and only if the symmetric function of degree n-1 of the principal curvatures of u is positive, and moreover, u fails to be when not smooth.  相似文献   

11.
12.
Monge-Ampère equation is a nonlinear equation with high degree, therefore its numerical solution is very important and very difficult. In present paper the numerical method of Dirichlet's problem of Monge-Ampère equation on Cartan-Hartogs domain of the third type is discussed by using the analytic method. Firstly, the Monge-Ampère equation is reduced to the nonlinear ordinary differential equation, then the numerical method of the Dirichlet problem of Monge-Ampère equation becomes the numerical method of two point boundary value problem of the nonlinear ordinary differential equation. Secondly, the solution of the Dirichlet problem is given in explicit formula under the special case, which can be used to check the numerical solution of the Dirichlet problem.  相似文献   

13.
The results by Palagachev (2009) [3] regarding global Hölder continuity for the weak solutions to quasilinear divergence form elliptic equations are generalized to the case of nonlinear terms with optimal growths with respect to the unknown function and its gradient. Moreover, the principal coefficients are discontinuous with discontinuity measured in terms of small BMO norms and the underlying domain is supposed to have fractal boundary satisfying a condition of Reifenberg flatness. The results are extended to the case of parabolic operators as well.  相似文献   

14.
In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.  相似文献   

15.
In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.  相似文献   

16.
By using the Leggett-Williams fixed point theorem, this paper investigates the existence of at least three nontrivial radial convex solutions of systems of Monge-Ampère equations.  相似文献   

17.
Summary We prove interior oscillation and global Hölder estimates, independent of any boundary data, for convex solutions of certain types of Monge-Ampère equations under suitable conditions on the equation and the domain n . We also deduce the existence, uniqueness, regularity and unboundedness, under suitable conditions, of convex extremal solutions of certain Monge-Ampère equations.  相似文献   

18.
In this paper, we obtain the Bedford-Taylor interior C2 estimate and local Calabi C3 estimate for the solutions to complex Monge-Ampère equations on Hermitian manifolds.  相似文献   

19.
We prove the minimum principle and the Poisson property for the potential theory of the homogeneous Monge-Ampère equation on a reflexive Banach space.  相似文献   

20.
We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension \(n\ge 3\), the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号