Gagliardo-Nirenberg inequalities on manifolds

We prove Gagliardo-Nirenberg inequalities on some classes of manifolds, Lie groups and graphs.Comment: 15 page

Magma Snolf at Rest

This piece is my attempt exercise agency in naming my identity: I am a Snolf

Real interpolation of Sobolev spaces

We prove that $W^{1}_{p}$ is an interpolation space between $W^{1}_{p_{1}}$ and $W^{1}_{p_{2}}$ for $p>q_{0}$ and $1\leq p_{1}<p<p_{2}\leq \infty$ on some classes of manifolds and general metric spaces, where $q_{0}$ depends on our hypotheses.Comment: 30 page

Squatting problems in Indonesia : a research study presented to the Institute of Development Studies, Massey University, Palmerston North - New Zealand in partial fulfilment for the degree of Master of Philosophy

Most of urban dwellers in developing countries have been squatting too long. This is a phenomenon also characteristic of Indonesia. Big cities like Jakarta and Surabaya attract rural people who migrate because of poverty pressure in rural areas. The national development programs in Indonesia have resulted in extraordinary economic growth. However, at the same time, these development policies have created some social imbalances which in turn have lead to and maintained the squatter settlement problem in the cities. This research finds that there are some policies that can be carried out in order to reduce these problems. Possible solutions are derived from both direct and indirect actions. Direct solutions should be associated with the squatters themselves, in which the policies are aimed to improve their condition, economically and socially. Finally, indirect solutions should be addressed to rural development and specifically, the control of unoccupied land. All in all, policies should be carried out both in urban areas where the problem of squatting exists and in the rural areas, being the main source of the problem

Sobolev spaces on multiple cones

The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from \RR^n. The analysis interestingly combines use of Poincar\'e inequalities and of some Hardy type inequalities.Comment: Modifications following the referee's suggestions. Some typos and math typos corrected. Addition of references to Poincar\'e inequalities on sphere