Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form »¡ 1=n μ ...1=n†...yn ¡ y0† μ »‡ 1=n, where ...1=n†...yn ¡ y0† is an estimate of the rotation number obtained from an orbit of length n with initial condition y0, and » is the true rotation number. This allows rotation numbers to be com...

We show that every bounded pseudo-convex domain with Hölder boundary in C n is hyperconvex.

For a general differential operator with smooth matrix-valued coefficients in a bounded domain with smooth boundary we consider the boundary properties of functions from the domain of definition of a maximal extension in L2(Ω) and we study the properties of extensions and boundary-value problems corresponding to them. The investigations are based on Green’s formula.

In this paper we consider an inverse boundary value problem of determining three dimensional unknown inclusions in an elliptic equation in a bounded domain Ω ⊂ R3 from finite boundary measurements on ∂Ω. We will show that polyhedral inclusions in Ω can be uniquely determined up to their convex edges from a single boundary measurement on ∂Ω.

We propose a novel technique, termed compact shape trees, for computing correspondences of single-boundary 2-D shapes in O(n) time. Together with zero or more features defined at each of n sample points on the shape’s boundary, the compact shape tree of a shape comprises the O(n) collection of vectors emanating from any of the sample points on the shape’s boundary to the rest of the sample poin...

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements is considered. An algorithm is given by using the fundamental solution.

In this paper, the artificial boundary method for Poisson problem in an infinite domain with a concave angle is investigated. The exact and approximate elliptical arc artificial boundary conditions are given. The finite element approximation is formulated in a bounded domain using the approximate artificial boundary condition and error estimates are obtained. Finally, some numerical examples sh...

We consider the Navier–Stokes system in a bounded domain with a smooth boundary. Given a time-dependent solution and an arbitrary open subset of the boundary, we prove the existence of a boundary control, supported in the given subset, that drives the system to the given solution in finite time.

This work is devoted to prove the existence of weak solutions of the kinetic Vlasov—Poisson— Fokker—Planck system in bounded domains for attractive or repulsive forces. Absorbing and reflectiontype boundary conditions are considered for the kinetic equation and zero values for the potential on the boundary. The existence of weak solutions is proved for bounded and integrable initial and boundar...