Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations

A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces

On semilinear elliptic equations with borderline Hardy potentials

In this paper we study the asymptotic behavior of solutions to an elliptic equation near the singularity of an inverse square potential with a coefficient related to the best constant for the Hardy inequality. Due to the presence of a borderline Hardy potential, a proper variational setting has to be introduced in order to provide a weak formulation of the equation. An Almgren-type monotonicity formula is used to determine the exact asymptotic behavior of solutions

A note on local asymptotics of solutions to singular elliptic equations via monotonicity methods

This paper completes and partially improves some of the results of [arXiv:0809.5002] about the asymptotic behavior of solutions of linear and nonlinear elliptic equations with singular coefficients via an Almgren type monotonicity formul

On the behavior at collisions of solutions to Schr\"odinger equations with many-particle and cylindrical potentials

The asymptotic behavior of solutions to Schr\"odinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of solutions to at most critical semilinear elliptic equations with cylindrical and quantum multi-body singular potentials. Furthermore, by an iterative Brezis-Kato procedure, point-wise upper estimate are derived.Comment: 61 page

Con l’incertezza di misura un giudice derubrica un reato di guida in stato di ebbrezza

Per la prima volta in Italia, per quanto a conoscenza degli autori, un reato per guida in stato di ebrezza è stato derubricato sulla base di considerazioni metrologiche e della valutazione d’incertezza a partire dalle specifiche di accuratezza fornite dal costruttore nel manuale operativo dello strumento in uso alle forze dell’ordine e non, come finora avvenuto, sulla base di una verifica dello strumento impiegato. Questo articolo discute le motivazioni giuridiche e metrologiche che hanno indotto il giudice a emettere la sentenza

A Metrological Approach to Ethical and Legal Issues in Artificial Intelligence

Artificial Intelligence has developed in an impressive way during the recent years, and is now being applied to almost every field of human activities, slowly replacing human beings in operations whose level of required skills has significantly increased. Collaborative robots, or cobots, are a reality in industrial production, as well as virtual reality and robots driven by human motions from remote sites allow operators to control operations in dangerous areas. AI algorithms perform data searches and present the results in a very efficient way, so that they are helping decision makers in critical fields, such as medicine and justice. This poses new and somehow unforeseen ethical and legal problems that must be covered to avoid generating wrong or even illegal results. Some of these wrong results might be generated by the use of input data that might not be sufficiently accurate, especially when they are collected from the field, or whose limited accuracy is not properly considered when processing them. This paper aims at considering a possible, metrologically-sound approach to ethical and legal issues met in AI