Liouville properties and critical value of fully nonlinear elliptic operators

We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in Ornstein- Uhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully nonlinear parabolic equations. The second is the solvability of an ergodic Hamilton-Jacobi-Bellman equation that identifies a unique critical value of the operator.Comment: 18 pp, to appear in J. Differential Equation

Modelling and control of a waste to energy plant : waste bed temperature control using a feedback control law

In this dissertation the waste incineration process has been described, an overview of the state of the art control methodologies given and a new approach, based on input/output linearization and extremum seeking has been presented. This approach has been tested on a model appositely designed. The results have shown that it is possible to control the waste bed temperature to certain reference values, with robustness against changes in the waste composition. It is furthermore possible to identify reference values for the waste bed temperature such as the steam ow rate is maximized, while at the same time fulfilling operational constraints

A Net Energy-based Analysis for a Climate-constrained Sustainable Energy Transition

The transition from a fossil-based energy economy to one based on renewable energy is driven by the double challenge of climate change and resource depletion. Building a renewable energy infrastructure requires an upfront energy investment that subtracts from the net energy available to society. This investment is determined by the need to transition to renewable energy fast enough to stave off the worst consequences of climate change and, at the same time, maintain a sufficient net energy flow to sustain the world's economy and population. We show that a feasible transition pathway requires that the rate of investment in renewable energy should accelerate approximately by an order of magnitude if we are to stay within the range of IPCC recommendations

Recommendations for the representation of hierarchical objects in Europeana

The issue of handling hierarchical objects has been always an important topic for Europeana’s network of projects and Data Providers. The implementation of solutions in the Europeana portal has been delayed for a long time mainly due to the fact that complex objects required the development of new functionalities that could not be supported by the Europeana Semantic Elements (ESE) model. Indeed the simplicity and the flatness of this model prevented Data Providers from supplying complex objects

Comparison Principles for subelliptic equations of Monge-Ampere type

We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group

Mean field games models of segregation

This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of MFG theory, in the stationary and in the evolutive case. Numerical methods are proposed with several simulations. In the examples and in the numerical results, particular emphasis is put on the phenomenon of segregation between the populations. </jats:p