Bøger af Luigi Ambrosio

This work is closely tied to the renowned mathematics textbook series known as UNITEXT, tailored for university students pursuing bachelor's or master's degrees. What sets this particular book apart in the Springer collection is its unique origin: it has been crafted through a meticulous process involving interviews handled with and by world-class mathematicians. The content featured in this book revolve around a highly relevant and engaging topic: Optimal Transport. These conversations involve not only authors from the UNITEXT series, but also members of the series' Editorial Board. Additionally, they feature prominent figures in the field, including a Field Medalist. This work provides readers with a snapshot of remarkable vitality and freshness, guaranteed to captivate and engage anyone with an interest in mathematics. It's important to note that these interviews were initially shared as podcasts and originally broadcasted as online events on the Cassyni platform. Subsequently, advanced AI tools were employed under human supervision to transcribe the audios and edit them for better readability. A human copy-editor was involved during the whole process, and the authors revised the final copy-edited texts before publication. The content in each format - the interviews, the PODCASTS and the book - is self-contained and not a mere adaptation from one medium to another. Instead, it represents an independent exploration of the subject matter.

Dieses Buch ist ein Muss für alle Kinder und Jugendlichen, die gerne spielen, lachen und neue Wörter lernen! Mit über 500 lustigen Wörtern und ihren Bedeutungen ist dieses Lexikon vollgepackt mit jeder Menge Spaß und Humor. Von "A wie Abenteurer" bis "Z wie Zylinder" bietet das Buch eine Fülle von witzigen Wortspielen, die die Fantasie anregen und die Kreativität fördern.Jedes Wort wird mit einer Definition und einer kurzen Geschichte oder einem Beispiel erklärt, das den Kontext veranschaulicht. Die Illustrationen und Bilder, die jedes Wort begleiten, sind voller Farbe und zeigen, wie viel Spaß das Wort haben kann.Dieses Lexikon ist nicht nur ein hervorragendes Werkzeug, um den Wortschatz der Kinder zu erweitern, sondern auch ein unterhaltsamer Begleiter für regnerische Tage oder lange Autofahrten. Es gibt so viel zu entdecken und zu lachen, dass Kinder es immer wieder zur Hand nehmen werden.Das witzige Wörterbuch für kleine Sprachkünstler ist ein unverzichtbares Werkzeug für Eltern, Lehrer und alle, die sich für die Bildung von Kindern und Jugendlichen einsetzen. Es ist ein Buch, das dazu beitragen wird, dass Kinder die Welt um sich herum mit einer spielerischen und kreativen Einstellung erkunden.

This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport.

Provides new characterizations of the curvature dimension condition in the context of metric measure spaces $(X,\mathsf d,\mathfrak m)$. The authors' approach takes into account suitable weighted action functionals, and uses the nonlinear diffusion semigroup induced by the $N$-dimensional entropy, in place of the heat flow

It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

This book contains the notes of an international summer school on Analysis in Metric Spaces. Koskela, Upper gradients and Poincare inequalities; Semmes, Derivatives and difference quotients for Lipschitz or Sobolev functions on various spaces; Wheeden, Some weighted Poincare estimates in spaces of homogenous type.

This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems.

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion.

With a historical overview by Elvira Mascolo

In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others.

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively.