Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

The purpose in this paper is to establish pointwise estimates for a class of convex functions on the Heisenberg group. An integral estimate for classical convex functions in terms of the Monge–Ampère operator det D2u was proved by Aleksandrov, see [3, Theorem 1.4.2]. Such estimate is of great importance in the theory of weak solutions for the Monge–Ampère equation, and its proof revolves around...

The main analytical ingredients of the first part of this paper are two independent results: a theorem on approximation of W 2,2 solutions of the Monge-Ampère equation by smooth solutions, and a theorem on the matching (in other words, continuation) of second order isometries to exact isometric embeddings of 2d surface in R. In the second part, we rigorously derive the Γ-limit of 3-dimensional ...

We transfer the celebrating Monge-Kontorovich problem in a bounded domain of Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear elliptic equation with 0−order term missing in its diffusion coefficients: A(x, F ′ x )F ′′ xx +B(y, F ′ y )F ′′ yy = C(x, y, F ′ x , F ′ y ) where A(., .) > 0, B(., .) > 0 and C are functions based on the initial distributions, F is an unkn...

We prove one decomposition theorem of complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets. 2000 Mathematics Subject Classification. Primary 32W20, 32U15

The problem of optimal transportation between a set of sources and a set of wells has become recently the object of new mathematical models generalizing the Monge-Kantorovich problem. These models are more realistic as they predict the observed branching structure of communication networks. They also define new distances between measures. The question arises of how these distances compare to th...

Aus den Rezensionen: This is a very well written survey of some topics in the geometry of the tetrahedron. Although the subject belongs to that 19th century monument that has been systematically neglected called oldfashioned geometry, the method of solution employed throughout the paper is that of linear algebra, and the paper can be read as making a brilliant point for the teaching of linear a...