On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Differential Inclusions and Viability Theory

We present a summary of the basic results on differential inclusions and viability theory. A comprehensive exposition of these two theories is the purpose of the book on the same subject by the authors

Verbano

L’obiettivo del progetto è la soluzione del problema Verbano tramite la scelta di una nuova regolazione e di oppurtuni interventi strutturali. Tale soluzione deve tendere a minimizzare i danni causati da eventi alluvionali tanto a monte quanto a valle, i danni indotti dalla mancata fornitura idrica agli utenti irrigui ed idroelettrici di valle e quelli subiti dalla navigazione e dal turismo quando si deprimono eccessivamente i livelli lacuali, senza trascurare, nel contempo, il mantenimento di un deflusso minimo nel Ticino, a valle dello sbarramento del Panperduto. In tale ricerca si dovranno ovviamente tener conto dei vincoli posti dalla capacità di smaltimento delle portate all’incile del lago e dalla necessità di mantenere attiva la sua naturale funzione di laminazione in occasione di eventi alluvionali che interessino anche il Po

On the Finsler metrics obtained as limits of chessboard structures

We study the geodesics in a planar chessboard structure with two values 1 and $\beta>1$. The results for a fixed structure allow us to infer the properties of the Finsler metrics obtained, with an homogenization procedure, as limit of oscillating chessboard structures.Comment: 31 pages, 15 figure

On the Euler-Lagrange equation for a variational problem: the general case II

In this paper we study the existence of a solution in Lloc() to the Euler\u2013Lagrange equation for the variational problem infu+W01()(ID(u)+g(u))dx(01) with D convex closed subset of Rn with non empty interior. By means of a disintegration theorem, we next show that the Euler\u2013Lagrange equation can be reduced to an ODE along characteristics, and we deduce that there exists a solution to Euler\u2013Lagrange different from 0 a.e. and satisfies a uniqueness property. These results prove a conjecture on the existence of variations on vector fields stated in Bertone and Cellina (On the existence of variations)

Ultrasound imaging classifications of thyroid nodules for malignancy risk stratification and clinical management : state of the art

Assessing the risk of malignancy in the thyroid with ultrasound (US) is crucial in patients with nodules, as it can aid in selecting those who should have a fine-needle aspiration (FNA) biopsy performed. Many studies have examined whether the US characteristics of thyroid nodules are useful indicators of histological malignancy. Overall, these investigations have identified a few US features that are significantly more frequent in malignant thyroid nodules which can be coalesced into a defining set to be used as an indicator of a higher risk of malignancy. Despite these efforts, none of these classifications have been widely adopted worldwide, and there are still conflicting recommendations from different institutions. Understanding the role and appropriate utilization of these systems could facilitate the effective interpretation and communication of thyroid US findings among referring physicians and radiologists. In this comprehensive review, we outline the major US classification systems of thyroid nodules published in the last few years

Optimal control for satellite attitude maneuvers. Volume 1 - Mathematical analysis

Mathematical analyses of suboptimal attitude maneuvering control for synchronous earth pointing satellite