Gradient of the single layer potential and quantitative rectifiability for general Radon measures

Altres ajuts: Acord transformatiu CRUE-CSICAltres ajuts: Gobierno Vasco IT-1247-19We identify a set of sufficient local conditions under which a significant portion of a Radon measure μ on with compact support can be covered by an uniformly n-rectifiable set, at the level of a ball such that . This result involves a flatness condition, formulated in terms of the so-called -number of B, and the -boundedness, as well as a control on the mean oscillation on the ball, of the operator. Here is the fundamental solution for a uniformly elliptic operator in divergence form associated with an matrix with Hölder continuous coefficients. This generalizes a work by Girela-Sarrión and Tolsa for the n-Riesz transform. The motivation for our result stems from a two-phase problem for the elliptic harmonic measure

Il crimen expilatae hereditatis negli studi di diritto criminale di Franco Gnoli

AbstractThe paper aims to outline some relevant aspects of Franco Gnoli’s methodology and lines of interest with regard to the historical emersion and legal definition of the crimen expilatae hereditatis. Particular attention is devoted to the identification of the notion of this crime and its area of application

On the density problem in the parabolic space

In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely $\mathbb{R}^{n+1}$ equipped with parabolic dilations. In particular we prove a Marstrand-Mattila rectifiability criterion for measures of general dimension, we provide a characterisation through densities of intrinsic rectifiable measures, and we study the structure of $1$-codimensional uniform measures. Finally, we apply some of our results to the study of a quantitative version of parabolic rectifiability: we prove that the weak constant density condition for a $1$-codimensional Ahlfors-regular measure implies the bilateral weak geometric lemma

Il licenziamento del dirigente nel lavoro privato

Abstract The research explores the topic of manager’s dismissal in order to determine his protection in case of employer’s withdrawal. The discussion first focuses on the definition of manager, together with the identification of the cases to which it applies. Then, the analysis addresses the regulation of manager’s dismissal. The manager - excluded from the law n. 604/1966 because of his fiduciary relationship with the entrepreneur - enjoys, however, an effective legal protection coming from collective bargaining, based on the controversial notion of “giustificatezza”. The thesis proceeds to define “giustificatezza” according to the orientations of the doctrine and the Courts. This leads to the conclusion that in Italy every worker benefits from a minimum set of protections against dismissal. In the last part, the research compares the regulation of manager’s dismissal in the Italian and the American law. In recent years, the latter has experienced a significant limitation of the at will rule, with the result of increasing the safety net for employees in case of dismissal. This suggests that every modern State perceives as a priority - inherent to his own status - to provide to employees legal protection against the dismissal