A second order local minimality criterion for the triple junction singularity of the Mumford-Shah functional

This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional

Piecewise constant reconstruction of damaged color images

A variational model for reconstruction of damaged color images is studied, in particular in the case where only finitely many colors are admissible for the reconstructed image. An existence result and regularity properties of minimizers are presented

Da usi civici a beni comuni : gli studi sulla proprietà collettiva nella medievistica e nella modernistica italiana e le principali tendenze internazionali

This paper aims to gather and summarize the studies on collective properties and the commons developed by historians of the Middle Ages and Early Modern times in Italy during the last two centuries. The paper also intends to focus on the influence of European and American literature on Italian historiography regarding the commons, with particular regard to the approaches of socioeconomic and environmental history. First, the paper focuses on the contributions and approaches of scholars of jurisprudence and of Medieval and Modern law. It also analyses the political and cultural context that provided the background for their research (§ 1). Secondly, it summarizes the main approaches of American social scientists on common pool resources – Garret Hardin’s Tragedy of the Commons and Elinor Ostrom’s Governing the Commons – as well as the chief environmental and eco-history contributions (§ 2). The paper then focuses on studies by historians of the Middle Ages and Early Modern times, analysing the most developed regional literature and the main contributions and collective works (§ 3), as well as the recent season of studies on the management of the commons (§ 4)

La 'costruzione' della Dogana dei Paschi di Siena in Maremma (1353-1419)

This paper, presenting the first outcomes of a doctoral research, aims to demonstrate that the Statute of the Dogana dei Paschi of Siena of 1419 was not the foundation act of this institution but was the end of a normative process begun by the Sienese commune in Maremma in 1353 and connected with the 14th century’s crisis. This process reorganized a land with a strong pastoral and transhumant tradition where Siena have conquered, during his century old expansion, many rights and commons of pasturage. Through the rich public Sienese records analysis we go over the construction of the Dogana during seventy years to show the administrative’s structures and the budget of this increasing fiscal and territorial control of transhumant flows, the influence over it of exogenous factors, the innovations, the causes and the outcomes of the many riformative periods

La storia agraria dal medioevo all’età moderna : una rassegna sulla storiografia degli ultimi venti anni in alcuni paesi europei

The paper aims to concisely present the trends of the rural and agrarian history of Middle Ages and Early Modern period in Europe during the last twenty years. After a brief introduction, the first three paragraphs analyze the recent research paths of the British, French, Belgian and Dutch historiographies, among the most lively on those themes. The fourth paragraph explains the general trends of European research through the analysis of the most active networks, international conferences and book series in refreshing literature and spreading new debates.L’articolo è una sintesi delle tendenze principali della storia rurale e dell’agricoltura in Europa degli ultimi venti anni, in particolare per l’ambito medievistico e modernistico. Dopo una breve introduzione nei primi tre paragrafi sono ricostruiti i recenti percorsi di ricerca della storiografia inglese, francese e belga-olandese, tra i più innovativi su questi temi. Nel quarto sono analizzate le tendenze storiografiche diffuse a livello europeo, osservando i network, le conferenze internazionali e le collane editoriali più attive nel rinnovamento degli studi e nella loro diffusione

I conflitti per il controllo delle risorse collettive in un’area di dogana (Toscana meridionale, XIV-XV secolo)

The paper aims to analyze the conflicts in access to collective resources(pastures) at local level, focusing on their relation with the State-building process. Southern Tuscany was conquered and became part of the State of Siena during the 14th-15th c. It was reorganized through the Dogana dei Paschi of Siena, a fiscal institution in charge of managing transhumant flows in that area. The related take over of collective rights of pasturages and common land carried on by Siena in 1353-1419 lead to new levels of conflict for the management of commons. As a consequence, it created new asymmetric relations between the communities, the city-commune and the transhumant shepherds, usually damaging the formers. Through the analysis of the public archival records of Siena and of those of some communities it is possible to show to what extent this process was strong and ground-breaking in plundering and re-distributing collective resources. The paper aims, furthermore, to suggest applying both the micro-historical as well as the new-institution-al approach to improve our understanding of socio-economic dynamics of commons within similar case-studies

On the Gamma Convergence of Functionals Defined Over Pairs of Measures and Energy-Measures

A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing the $\Gamma$-limit of the underlining energies. In particular, the interaction between the functionals and the underlining energies results, in the case these latter converge to a non continuous energy, in an additional effect in the relaxation process. This study was motivated by a question in the context of epitaxial growth evolution with adatoms. Interesting cases of application of the general theory are also presented

On local and global minimizers of some non-convex variational problems

Many physical systems are modeled mathematically as variational problems, where the observed configurations are expected to be local or global minimizers of a suitable energy. Such an energy can be very complicated, as well as the physical phenomenon under investigation. Thus, as a starting point, it is useful to focus on some simple models, which however capture the main features. In this thesis we concentrate on two kinds of energies, that can be both viewed as nonlocal variants of the perimeter functional. The nonlocality consists in a bulk term, that in one case is given by an elastic energy, while in the other by a long-range interaction of Coulumbic type. The physical systems modeled by these energies displays a rich variety of observable patterns, as well as the formation of morphological instabilities of interfaces between different phases. These phenomena can be mathematically understood as the competition between the local geometric part of the energy, i.e., the perimeter, and the nonlocal one. Indeed, while the first one prefers configurations in which the interfaces are regular and as small as possible, the latter, instead, favors more irregular and oscillating patterns. Thus, finding global or local minima of these energies is a highly nontrivial task, and indeed many big issues about them are still open. The aim of this thesis is to give a contribution to the investigation of such issues