共查询到20条相似文献,搜索用时 15 毫秒
1.
Erhard Heinz Ralf Beyerstedt 《Calculus of Variations and Partial Differential Equations》1994,2(2):241-247
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
2.
The main result of this article is the existence and uniqueness of the solution of the Dirichlet problem for quaternionic
Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in ℍ
n
. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2]. 相似文献
3.
In this paper we are concerned with the global regularity of solutions to the Dirichlet problem for a class of Monge-Ampère type equations.By employing the concept of(a,η) type domain,we emphasize that the boundary regularity depends on the convexity of the domain in nature.The key idea of our proof is to provide more effective global H?lder estimates of convex solutions to the problem based on carefully choosing auxiliary functions and constructing sub-solutions. 相似文献
4.
Robert J. Berman Sébastien Boucksom Vincent Guedj Ahmed Zeriahi 《Publications Mathématiques de L'IHéS》2013,117(1):179-245
We show that degenerate complex Monge-Ampère equations in a big cohomology class of a compact Kähler manifold can be solved using a variational method, without relying on Yau’s theorem. Our formulation yields in particular a natural pluricomplex analogue of the classical logarithmic energy of a measure. We also investigate Kähler-Einstein equations on Fano manifolds. Using continuous geodesics in the closure of the space of Kähler metrics and Berndtsson’s positivity of direct images, we extend Ding-Tian’s variational characterization and Bando-Mabuchi’s uniqueness result to singular Kähler-Einstein metrics. Finally, using our variational characterization we prove the existence, uniqueness and convergence as k→∞ of k-balanced metrics in the sense of Donaldson both in the (anti)canonical case and with respect to a measure of finite pluricomplex energy. 相似文献
5.
Ph. Delanoë 《manuscripta mathematica》1983,45(1):29-45
In [4] (Theorem 2), we solved a Monge-Ampère equation, on a compact Riemannian manifold, which isnot a priori locally invertible. In particular, one cannot expect the solution to be unique. We investigate here, the way bifurcation phenomena may occur in such a case, with some explicit computations on flat tori. 相似文献
6.
John I. E. Urbas 《Inventiones Mathematicae》1988,91(1):1-29
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
7.
Feida Jiang Neil S. Trudinger Xiao-Ping Yang 《Calculus of Variations and Partial Differential Equations》2014,49(3-4):1223-1236
In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Ampére type equations under sharp hypotheses. In particular we assume that the matrix function in the augmented Hessian is regular in the sense used by Trudinger and Wang in Ann. Scoula Norm. Sup. Pisa Cl. Sci. VIII, 143–174 2009 in their study of global regularity in optimal transportation as well as the existence of a smooth subsolution. The latter hypothesis replaces a barrier condition also used in their work. The applications to optimal transportation and prescribed Jacobian equations are also indicated. 相似文献
8.
9.
John Urbas 《Mathematische Zeitschrift》2001,236(3):625-641
We derive a monotonicity formula for smooth solutions u of degenerate two dimensional Monge-Ampère equations, and use this to obtain a local H?lder gradient estimate, depending
on for some .
Received August 9, 1999; in final form December 8, 1999/ Published online December 8, 2000 相似文献
10.
Approximation of solutions of the Monge-Ampère equations by surfaces reduced to developable surfaces
L. B. Pereyaslavskaya 《Journal of Mathematical Sciences》2008,149(1):996-1020
We consider an approximate construction of the surface S that is the graph of a C
2-smooth solution z = z(x, y) of the parabolic Monge-Ampère equation
of special form with the initial conditions
, where a = a(y) and b = b(y) are given functions. In the method proposed, the desired solution is approximated by a sequence of C
1-smooth surfaces {S
n} each of which consists of parts of surfaces reduced to developable surfaces. In this case, the projections of characteristics
of the surface S that are curved lines in general are approximated by characteristic projections of the surfaces S
n that are polygonal lines composed of n links. The results of these constructions are formulated in the theorem. Sufficient conditions for the convergence of the
family of surfaces S
n to the surface S as n → ∞ are presented; this allows one to construct a numerical solution of the problem with any accuracy given in advance.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 205–236, 2006. 相似文献
11.
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
12.
We first define molecules for Hardy spaces
H1F(\mathbbRn)H^{1}_{\mathcal{F}}(\mathbb{R}^{n}) associated with a family F\mathcal{F} of sections which is closely related to the Monge-Ampère equation and prove their molecular characters. As an application,
we show that Monge-Ampère singular operators are bounded on
H1F(\mathbbRn)H^{1}_{\mathcal{F}}(\mathbb{R}^{n}). 相似文献
13.
14.
15.
Luis A. Caffarelli & Yu Yuan 《分析论及其应用》2022,38(2):121-127
We construct merely Lipschitz and $C^{1,α}$ with rational $α ∈ (0, 1 − 2/n]$ viscosity solutions to the Monge-Ampère equation with constant right hand side. 相似文献
16.
V. Ushakov 《Commentarii Mathematici Helvetici》2000,75(1):125-133
The general solution of the equation with minimal smoothness requirements is presented in explicit form; it depends on 2 functions of one variable. In particular, it allows to describe explicitly all developable surfaces (without planar points) in . The domain and singularities of the solution are investigated. Received: January 5, 1998 相似文献
17.
18.
Masafumi Yoshino 《偏微分方程通讯》2013,38(9-10):1925-1950
We study the global solvability of Monge-Ampère equations of mixed type by "blowing up" the problem onto the torus embedded at the singular point of the equations 相似文献
19.
对一类Monge-Amp(e)re方程的特征值问题进行了研究.通过移动平面法证明了在凸对称区域内,Dirichlet问题的C2凹(凸)解一定是对称的.进而通过对常微分方程和椭圆形偏微分方程的讨论,得到一类n维单位球上特征值问题的非平凡解的存在性和正则性结果. 相似文献
20.
王伟叶 《数学年刊A辑(中文版)》2007,(3)
对一类Monge-Ampère方程的特征值问题进行了研究.通过移动平面法证明了在凸对称区域内,Dirichlet问题的C~2凹(凸)解一定是对称的.进而通过对常微分方程和椭圆形偏微分方程的讨论,得到一类n维单位球上特征值问题的非平凡解的存在性和正则性结果. 相似文献