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This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advan...

This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been referred to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites forthe treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is ...

This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, andGromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discu...

Keine Beschreibung.

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. 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.

Biomedical Composites, Second Edition, provides revised, expanded, and updated content suitable for those active in the biomaterials and bioengineering field. Three new chapters cover modeling of biocomposites, 3D printing of customized scaffolds, and constructs and regulatory issues. Chapters from the first edition have been revised in order to provide up-to-date, comprehensive coverage of developments in the field. Part One discusses the fun...

Biomedical composites provides a thorough review of the current status, recent progress and future trends in composites for biomedical applications.

Keine Beschreibung.

These notes originated from a course given by the first author in 1998/99 in the Scuola Normale Superiore of Pisa. The aim of the course was the presentation of the main mathematical prerequisites needed for the so-called Analysis in Metric Spaces. The exposition, though not fully self contained, covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems, Sobolev spaces, all these topics are developed in a gener...

A review of spine biology and biomechanics, the latest developments in spinal biomaterials such as cages, plates and discs, and developments in regeneration of the spine. Chapters include biomechanics on the spine, disc replacement, vertebroplasty and scoliosis surgery.

In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. 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.This book presents an extensive set of notes by world leaders on the main mathematical techniques ...

In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone.The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperim...

This volume consists of eight original survey papers written by invited lecturers in connection with a conference "Variational Methods for Evolving Objects”. The topics of papers vary widely from problems in image processing to dynamics of topological defects, and all involve some nonlinear phenomena of current major research interests.

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. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates ...

In 2008, a school on the theory of Optimal Transportation and its applications took place in Pisa, with lectures by F. Barthe, W. Gangbo, F. Maggi, R. McCann. In this book, the notes of the first three lecturers are collected. They provide a deep insight on concentration inequalities, evolution PDEs of Hamiltonian type, geometric and functional inequalities.

Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models...