Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.

Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

A sharp concentration inequality with applications

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Narrowing socioeconomic inequality in child stunting: the Brazilian experience, 1974–2007

Objective To assess trends in the prevalence and social distribution of child stunting in Brazil to evaluate the effect of income and basic service redistribution policies implemented in that country in the recent past. Methods The prevalence of stunting (height-for-age z score below \22122 using the Child Growth Standards of the World Health Organization) among children aged less than 5 years was estimated from data collected during national household surveys carried out in Brazil in 1974\201375 (n = 34 409), 1989 (n = 7374), 1996 (n = 4149) and 2006\201307 (n = 4414). Absolute and relative socioeconomic inequality in stunting was measured by means of the slope index and the concentration index of inequality, respectively. Findings Over a 33-year period, we documented a steady decline in the national prevalence of stunting from 37.1 per cent to 7.1 per cent. Prevalence dropped from 59.0 per cent to 11.2 per cent in the poorest quintile and from 12.1 per cent to 3.3 per cent among the wealthiest quintile. The decline was particularly steep in the last 10 years of the period (1996 to 2007), when the gaps between poor and wealthy families with children under 5 were also reduced in terms of purchasing power; access to education, health care and water and sanitation services; and reproductive health indicators.Conclusion In Brazil, socioeconomic development coupled with equity-oriented public policies have been accompanied by marked improvements in living conditions and a substantial decline in child undernutrition, as well as a reduction of the gap in nutritional status between children in the highest and lowest socioeconomic quintiles. Future studies will show whether these gains will be maintained under the current global economic crisis

On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

Non-Spatial Government Policies and Regional Income Inequality in Brazil

Silveira Neto R. Da M. and Azzoni C. R. Non-spatial government policies and regional income inequality in Brazil, Regional Studies. This paper uses both macro- and micro-data to analyse the role of social programmes in the recent reduction in Brazilian regional income inequality. Convergence indicators are presented for different sources of regional income in the period 1995-2006. A decomposition of the Gini indicator allows the identification of the role of each of these income sources with respect to the reduction of regional inequality during the period. The results point out that both labour productivity and government non-spatial policies - mainly minimum wage changes and income transference programmes - do have a role in explaining regional inequality reduction during the period. [image omitted] Silveira Neto R. Da M. et Azzoni C. R. Les politiques gouvernementales non-spatiales et l`ecart des revenus regionaux au Bresil, Regional Studies. Cet article emploie des donnees a la fois macroeconomiques et microeconomiques afin d`analyser le role des programmes d`actions sociales quant a la baisse recente de l`ecart des revenus regionaux au Bresil. On presente des indicateurs de convergence pour diverses sources des revenus regionaux pour la periode allant de 1995 a 2006. Une decomposition du coefficient de Gini permet d`identifier le role de chacune de ces sources des revenus par rapport a la baisse de l`ecart des revenus pendant cette periode. Les resultats indiquent que la productivite du travail et les politiques gouvernementales non-spatiales - notamment la modification du salaire minimum et les programmes visant le transfert des revenus - ont un role a jouer pour expliquer la baisse de l`ecart des revenus regionaux pendant la periode en question. Convergence Productivite du travail Transfert des revenus Salaire minimum Effets spatiaux des politiques non-spatiales Silveira Neto R. Da M. und Azzoni C. R. Nicht raumliche Regierungspolitiken und das regionale Einkommensungleichgewicht in Brasilien, Regional Studies. In diesem Beitrag analysieren wir mit Hilfe von Makro- und Mikrodaten die Rolle von sozialen Programmen bei der unlangst erzielten Verringerung des regionalen Einkommensungleichgewichts in Brasilien. Wir stellen Konvergenz-Indikatoren fur verschiedene regionale Einkommensquellen im Zeitraum von 1995 bis 2006 vor. Eine Dekomposition des Gini-Indikators ermoglicht die Identifizierung der jeweiligen Rolle dieser Einkommensquellen fur die Verringerung des regionalen Ungleichgewichts im betreffenden Zeitraum. Die Ergebnisse weisen darauf hin, dass sowohl die Produktivitat der Arbeitskrafte als auch die nicht raumlichen Regierungspolitiken - in erster Linie Veranderungen beim Mindestlohn und Programme fur Einkommenstransfers - als Grunde fur die Verringerung des regionalen Ungleichgewichts in dieser Periode durchaus eine Rolle spielen. Konvergenz Arbeitsproduktivitat Einkommenstransfer Mindestlohn Raumliche Auswirkungen nicht raumlicher Politiken Silveira Neto R. Da M. y Azzoni C. R. Politicas gubernamentales no espaciales y desigualdades de ingresos regionales en Brasil, Regional Studies. En este articulo utilizamos datos macro y micro para analizar el papel de los programas sociales en la reciente reduccion en las desigualdades de ingresos regionales de Brasil. Presentamos los indicadores de convergencia para diferentes fuentes de ingresos regionales en el periodo de 1995 a 2006. Una descomposicion del indice Gini permite identificar el papel de cada una de estas fuentes de ingresos con respecto a la reduccion de las desiguadades regionales durante este periodo. Los resultados destacan que tanto la productividad laboral como las politicas no espaciales del gobierno - principalmente los cambios de salario minimo y los programas de transferencias de ingresos - desempenan una funcion a la hora de explicar la reduccion de las desigualdades regionales durante este periodo. Convergencia Productividad laboral Transferencias de ingresos Salario minimo Efectos espaciales de politicas no espaciales.

Income inequality and pecuniary crimes

This paper verifies the relationship between income inequality and pecuniary crimes. The elasticity of pecuniary crimes relative to inequality is 1.46, corroborating previous literature. Other factors important to decrease criminality are expanding job opportunities and a more efficient legal system, (C) 2009 Elsevier B.V. All rights reserved.

Income inequality and male homicide rates: Sao Paulo, Brazil, 1996-2007

In Sao Paulo, Brazil, homicides to men aged 15-44 years increased with an annual percentage change (APC) of 4.7% from 1996 to 2001, and then decreased from 2001 to 2007 with an APC of -14.6%. Analyzing the intra-urban distribution according to family income, the increase in the homicide rate was restricted to men living in the poorest neighbourhoods. In contrast, the decline in homicide rates was observed to men living in all districts. The reasons for this `up and down` trend are not clear.