Finite speed of propagation for a non-local porous medium equation

This note is concerned with proving the finite speed of propagation for some non-local porous medium equation by adapting arguments developed by Caffarelli and V\'azquez (2010).Comment: 10 pages. New version after revision. Several typos removed and more explainations given the contact analysi

Level set approach for fractional mean curvature flows

This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set. Moreover the associated flow appears in two important applications: dislocation dynamics and phase field theory for fractional reaction-diffusion equations. It is defined by using the level set method. The main results of this paper are: on one hand, the proper level set formulation of the geometric flow; on the other hand, stability and comparison results for the geometric equation associated with the flow

Decomposing wage inequality: Public and private sectors in Vietnam 1993-2006

This paper studies the labor market in Vietnam during the transition towards market economy (1993-2006): we show that the public-private sector wage gap markedly increased, but that wage inequality decreased overall. Our aim is to assess how much of this evolution can be explained by workers' productive skills and their allocation between sectors. We use a simple, yet innovative, method that allows us to take into account workers' unobservable characteristics and their remuneration in each sector. Throughout the period we consider, public sector workers are more skilled than private sector workers. However, rising returns to workers' skills in the public sector play a major role in the increase of the public-private sector gap. Against all expectations, the public sector grew richer as Vietnam moved towards market economy. Finally, a greater homogeneity among labor market participants seems to explain the overall decline in wage inequality.transition ; inequality decomposition ; public sector

Self-similar solutions for a fractional thin film equation governing hydraulic fractures

In this paper, self-similar solutions for a fractional thin film equation governing hydraulic fractures are constructed. One of the boundary conditions, which accounts for the energy required to break the rock, involves the toughness coefficient $K\geq 0$. Mathematically, this condition plays the same role as the contact angle condition in the thin film equation. We consider two situations: The zero toughness ($K=0$) and the finite toughness $K\in(0,\infty)$ cases. In the first case, we prove the existence of self-similar solutions with constant mass. In the second case, we prove that for all K\textgreater{}0 there exists an injection rate for the fluid such that self-similar solutions exist

The Schauder estimate in kinetic theory with application to a toy nonlinear model

This article is concerned with the Schauder estimate for linear kinetic Fokker-Planck equations with H\"older continuous coefficients. This equation has an hypoelliptic structure. As an application of this Schauder estimate, we prove the global well-posedness of a toy nonlinear model in kinetic theory. This nonlinear model consists in a non-linear kinetic Fokker-Planck equation whose steady states are Maxwellian and whose diffusion in the velocity variable is proportional to the mass of the solution

Costs and benefits of rural-urban migration : evidence from India

This paper provides new evidence on rural-urban migration decisions in developing countries. Using original survey data from rural India, we show that seasonal migrants prefer to earn 35 percent less on local public works rather than incur the cost of migrating. Structural estimates suggest that the fixed cost of migration is small, and can be entirely explained by travel costs and income risk. In contrast, the flow cost of migration is high. We argue that higher living costs in the city explain only a small part of the flow cost of migration and that most of it is non-monetary

Estimates on elliptic equations that hold only where the gradient is large

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the H{\"o}lder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.Comment: 18 page