Ronald J. Allen & O. Wesley Allen Jr., The Sermon without End: A Conversational Approach to Preaching

Multiple-end Solutions to the Allen-cahn Equation in R

We construct new class of entire solutions of the Allen-Cahn equation ∆u+(1−u2)u = 0, in R2(∼ C). Given k ≥ 1, we find a family of solutions whose zero level sets are, away from a compact set, asymptotic to 2k straight lines (which we call the ”ends”). These solutions have the property that there exists θ0 < θ1 < . . . < θ2k = θ0 + 2π such that limr→+∞ u(re iθ) = (−1)j uniformly in θ on compact...

Two-end solutions to the Allen-Cahn equation in R

has been studied for several decades and is an important nonlinear PDE due to the fact that it lies at the interface of several different mathematical fields. The famous De Giorgi conjecture states that any entire solution to (1) in R which is monotone in one direction should be one dimensional, at least for n ≤ 8. The conjecture was proved in dimension n = 2 by Ghoussoub-Gui ([13]) and dimensi...

A relaxation approach to vector-valued Allen-Cahn MPEC problems

In this paper we consider a vector-valued Allen-Cahn MPEC problem. To derive optimality conditions we exploit a regularization-relaxation technique. The optimality system of the regularized-relaxed subproblems are investigated by applying the classical result of Zowe and Kurcyusz. Finally we show that the stationary points of the regularizedrelaxed subproblems converge to weak stationary points...

Allen Schick

During the past decade New Zealand has introduced far-reaching reforms in the structure and operation of government departments and agencies. This model has attracted interest in developing countries because it promises significant gains in operational efficiency. But developing countries, which are dominated by informal markets, are risky candidates for applying the New Zealand model. The auth...

Natalie Allen