Economy and environment: Issues on transport externalities, CO2 responsibility and environmental Kuznets curve

In this thesis some of the most important issues presently debated on international sustainability are analysed. The thesis is composed of five independent studies that tackle organically the following issues: the maritime transport externalities, the environmental Kuznets curve, the responsibilities in the carbon dioxide emissions and the integrated approach that have to be used to translate the principles of sustainability into policy. The analysis will be instrumental to demonstrating that sustainability, being a matter of economy, society and environment, requires to be analysed in a transdisciplinary perspective. Using an integrated approach to analyse the relationships between economy and environment, this thesis highlight that sustainability management requires joint economic instruments, integrated analysis, societal behavioural changes as well as responsibilities shifting.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.