The p-Laplace equation in domains with multiple crack section via pencil operators

The p-Laplace equation \n \cdot (|\n u|^n \n u)=0 \whereA n>0, in a bounded domain \O \subset \re^2, with inhomogeneous Dirichlet conditions on the smooth boundary \p \O is considered. In addition, there is a finite collection of curves \Gamma = \Gamma_1\cup...\cup\Gamma_m \subset \O, \quad \{on which we assume homogeneous Dirichlet boundary conditions} \quad u=0, modeling a multiple crack formation, focusing at the origin 0 \in \O. This makes the above quasilinear elliptic problem overdetermined. Possible types of the behaviour of solution $u(x,y)$ at the tip 0 of such admissible multiple cracks, being a "singularity" point, are described, on the basis of blow-up scaling techniques and a "nonlinear eigenvalue problem". Typical types of admissible cracks are shown to be governed by nodal sets of a countable family of nonlinear eigenfunctions, which are obtained via branching from harmonic polynomials that occur for $n=0$. Using a combination of analytic and numerical methods, saddle-node bifurcations in $n$ are shown to occur for those nonlinear eigenvalues/eigenfunctions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.065

The system of landholding in Hong Kong

In this article we analyse the history of land dealing in Hong Kong from 1843 onwards and also its current situation. Almost all land in Hong Kong vests in the State and there is, with the exception of St. John's Cathedral, no privately owned freehold land in Hong Kong. We also study how Land Law operates in the New Territories and also a very important topic: what will happen to Property and Land Rights after 2047? At last, a briefcomparison with the Spanish system of landholding is made in order to see the main differences of both systems

A Comparison of the System of Public Housing in Hong Kong with the System of Public Housing in Spain

The goal of this paper is to briefly study the system of Public Housing in Hong Kong and Spain, and to compare them. On the one hand, Hong Kong has more than 7.2 million residents crammed into a relatively small land mass, a fact which, among others, provokes that real estate prices are extremely high. Because of the high prices, the Government has had to introduce a large system of public housing (almost a 46% of Hong Kong’s population lives under some of the Public Housing Schemes). On the other hand, in Spain, even though Public Housing has a constitutional basis, the system remains still very inefficient and far less important than in Hong Kong