On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary

in this paper we investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev exponents on the right-hand side of the equation and in the boundary condition. It is assumed that the coefficients Q and P are smooth. We examine the common effect of the mean curvature of the boundary a deltaOhm and the shape of the graph of the coefficients Q and P on the existence of solutions of problem (1.1). (C) 2003 Published by Elsevier Inc.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

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.

On multiple solutions of the exterior neumann problem involving critical sobolev exponent

In this paper we consider the exterior Neumann problem involving a critical Sobolev exponent. We establish the existence of two solutions having a prescribed limit at infinity.

Influence of adsorbate interaction on transport in confined spaces

This article provides a review of the recent theory of transport in nanopores developed in the author's laboratory. In particular the influence of fluid-solid interactions on the transport coefficient is examined, showing that such interactions reduce the value of the coefficient by almost an order of magnitude in comparison to the Knudsen theory for non-interacting systems. The activation energy and potential energy barriers for diffusion in smooth pores with a one-dimensional potential energy profile are also discussed, indicating the inadequacy of the commonly used assumption of proportionality between the activation energy and heat of adsorption or the minimum pore potential energy. A further feature affected by fluid-solid interactions is the nature of the reflection of fluid molecules colliding with a pore wall surface, varying from being nearly specular - such as in carbon nanotubes - to nearly diffuse for amorphous solids. Diffuse reflection leads to momentum loss and reduced transport coefficients. However, fluid-solid interactions do not affect the transport coefficient in the single-file diffusion regime when the surface reflection is diffuse, and the transport coefficient in this case is largely independent of the adsorbed density.

Neighborhood environmental factors correlated with walking near home: Using SPACES

Purpose: The physical environment plays an important role in influencing participation in physical activity, although the specific factors that are correlated with different patterns of walking remain to be determined We examined correlations between physical environmental factors and self-reported walking for recreation and transport near home. Methods: The local neighborhood environments (defined as a 400-m radius from the respondent's home) of 1678 adults were assessed for their suitability for walking. The environmental data were collected during 2000 using the Systematic Pedestrian and Cycling Environmental Scan (SPACES) instrument together with information from other sources. We used logistic regression modeling to examine the relationship between the attributes of the physical environment and the self-reported walking behavior undertaken near home. Results: Functional features were correlated with both walking for recreation (odds ratio (OR) 1.62; 95% confidence interval (Cl): 1.20-2.19) and for transport (OR 1.30; 95% Cl: 0.97-1.73). A well-maintained walking surface was the main functional factor associated with walking for recreation (OR 2.04; 95% Cl: 1.43-2.91) and for transport (OR 2.13; 95% Cl: 1.53-2.96). Destination factors, such as shops and public transport, were significantly correlated with walking for transport (OR 1.80; 95% Cl: 1.33-2.44), but not recreation. Conclusion: The findings suggest that neighborhoods with pedestrian facilities that are attractive and comfortable and where there are local destinations (such as shops and public transport) are associated with walking near home.