Reflection and the Neumann problem on doubly connected regions

Time-dependent conformal mapping of doubly-connected regions

This paper examines two key features of time-dependent conformal mappings in doubly-connected regions, the evolution of the conformal modulus Q(t) and the boundary transformation generalizing the Hilbert transform. It also applies the theory to an unsteady free surface flow. Focusing on inviscid, incompressible, irrotational fluid sloshing in a rectangular vessel, it is shown that the explicit ...

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

The Neumann Problem on Lipschitz Domains

Au — 0 in D; u = ƒ on bD9 where ƒ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. Calderón et al. [1]. For dimension 2, see (d) below. In [4] and [5] we found an elementary integral formula (7) and used it to prove a theorem of Dahlberg (Theorem 1) on Lipschitz domains. Unknown to us, this formula had already been discovered long ago by Payne and We...

On the Von Neumann Economic Growth Problem

Numerical Conformal Mapping of Doubly Connected Regions via the Kerzman-stein Kernel

Abstract: An integral equation method based on the Kerzman-Stein kernel for conformal mapping of smooth doubly connected regions onto an annulus A = {w : μ < |w| < 1} is presented. The theoretical development is based on the boundary integral equation for conformal mapping of doubly connected regions with Kerzman-Stein kernel derived by Razali and one of the authors [8]. However, the integral e...