A nonlinear elliptic problem with terms concentrating in the boundary

In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a $\epsilon$-neighborhood of a portion $\Gamma$ of the boundary. We assume that this $\epsilon$-neighborhood shrinks to $\Gamma$ as the small parameter $\epsilon$ goes to zero. Also, we suppose the upper boundary of this $\epsilon$-strip presents a highly oscillatory behavior. Our main goal here is to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on $\Gamma$, which depends on the oscillating neighborhood

Addressing food and nutrition security in South Africa: A review of policy responses since 2002

Since 2002, a range of South African policies have attempted to address the disproportionate burden of food and nutrition insecurity on the population. Yet malnutrition among the poor has worsened. This study reviewed policies to examine their implications for food security and the treatment of malnutrition. Policies enacted between 2002 and 2017 were retrieved from government departments and the data were thematically analysed. A preliminary analysis shows that policy has aided production through input provision and capacity building. Taxation, school nutrition programmes and social grants are some of the food access initiatives, whilst micronutrient supplementation, breastfeeding campaigns and food fortification are policies specifically focused on nutrition. However, despite these interventions, food insecurity has remained due to gaps in and contradictions among policies and the lack of coordination in policy development and implementation, especially across sectors. To improve food and nutrition security, government must better engage with ideas about how to address food and nutrition security systemically, and develop the appropriate coordination mechanisms for a more holistic approach to this challenge

Isotropization of the universe during inflation

A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the observational consequences of a possible early anisotropic phase? We first review the dynamics of anisotropic universes and report analytic approximations. We then discuss the structure of dynamical equations for perturbations and the statistical properties of observables, as well as the implication of a primordial anisotropy on the quantization of these perturbations during inflation. Finally we briefly review models based on primordial vector field which evade the cosmic no-hair theorem.Comment: 9 pages, 3 figures. Invited review article for the French Academy of Scienc