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.

Fekete-Szegö Inequality for Universally Prestarlike Functions

MSC 2010: 30C45

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

Documenting reproduction and inequality : revisiting Jean Anyon’s “Social class and school knowledge”

Jean Anyon’s (1981) “Social class and school knowledge” was a landmark work in North American educational research. It provided a richly detailed qualitative description of differential, social-class-based constructions of knowledge and epistemological stance. This essay situates Anyon’s work in two parallel traditions of critical educational research: the sociology of the curriculum and classroom interaction and discourse analysis. It argues for the renewed importance of both quantitative and qualitative research on social reproduction and equity in the current policy context.

Action research for contexts of change and inequality

Undoubtedly, the past half-century has witnessed an escalation of changes in the social, political, economic and educational structures in many societies around the world. Some have seen change as a challenge and hope while, for many others, it is a source of concern and worry. Some have adopted change with gusto, while for many it is something to be resisted. Some say we live in a world and times with an increasing awareness that “times are changing”, while for some “the more things change, the more they stay the same”.

Health, endogenous time preference, and inequality : a political economy perspective

We study an overlapping-generations model in which agents' mortality risks, and consequently impatience, are endogenously determined by private and public investment in health care. Revenues allocated for public health care arc determined by a voting process. We find that the degree of substitutability between public and private health expenditures matters for macroeconomic outcomes of the model. Higher substitutability implies a “crowding-out" effect, which in turn impacts adversely on morality risks and impatience leading to lower public expenditures on health care in the political equilibrium. Consequently, higher substitutability is associated with greater polarization in wealth, and long-run distributions that are bimodal.