Luigi Ambrosio – författare

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 fundamentals of biocomposites, with Part Two detailing a wide range of applications of biocomposites. Chapters in Part Three discuss the biocompatibility, mechanical behavior, and failure of biocomposites, while the final section looks at the future for biocomposites.

Professor Luigi Ambrosio is the Director of the Institute for Composite and Biomedical Materials, Italy. He is a renowned scientist with expertise in biomedical composites and has published over 150 papers in international scientific journals and books, 16 patents, and over 250 presentations at international and national conferences.

Led by an expert editor with many years of experience in academia and widely recognized as an international expert on biomedical composites Features an overview of biocomposites for a wide range of biomedical applications Provides revised, expanded, and updated coverage, including three new chapters

Electrofluidodynamic Technologies (EFDTs) for Biomaterials and Medical Devices: Principles and Advances focuses on the fundamentals of EFDTs - namely electrospinning, electrospraying and electrodynamic atomization - to develop active platforms made of synthetic or natural polymers for use in tissue engineering, restoration and therapeutic treatments. The first part of this book deals with main technological aspects of EFDTs, such as basic technologies and the role of process parameters. The second part addresses applications of EFDTs in biomedical fields, with chapters on their application in tissue engineering, molecular delivery and implantable devices. This book is a valuable resource for materials scientists, biomedical engineers and clinicians alike.

Presents a complete picture of Electrofluidodynamic technologies and their use in biomedicine Provides a comprehensive, professional reference on the subject, covering materials processing, fabrication and the use of novel devices for tissue engineering and therapeutics Focuses on technological advances, with an emphasis on studies and clinical trials

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 refered to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is introduced to the theory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the Mumford-Shah image segmentation problem. Existence, regularity and qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. Free discontinuity problems reveal a wide range of applications. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principle contributors to the theory. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory, that is Abstract Measure Theory and Geometric Measure Theory.

Based on lecture notes from the Scuola Normale this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers. The book covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed in a general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed in general metric spaces and, as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using Cavalieri's formula as the definition of the integral.

There have been important developments in materials and therapies for the treatment of spinal conditions. Biomaterials for spinal surgery summarises this research and how it is being applied for the benefit of patients.After an introduction to the subject, part one reviews fundamental issues such as spinal conditions and their pathologies, spinal loads, modelling and osteobiologic agents in spinal surgery. Part two discusses the use of bone substitutes and artificial intervertebral discs whilst part three covers topics such as the use of injectable biomaterials like calcium phosphate for vertebroplasty and kyphoplasty as well as scoliosis implants. The final part of the book summarises developments in regenerative therapies such as the use of stem cells for intervertebral disc regeneration.With its distinguished editors and international team of contributors, Biomaterials for spinal surgery is a standard reference for both those developing new biomaterials and therapies for spinal surgery and those using them in clinical practice.Summarises recent developments in materials and therapies for the treatment of spinal conditions and examines how it is being applied for the benefit of patientsReviews fundamental issues such as spinal conditions and their pathologies, spinal loads, modelling and osteobiologic agents in spinal surgeryDiscusses the use of bone substitutes and artificial intervertebral discs and covers topics such as the use of injectable biomaterials like calcium phosphate for vertebroplasty and kyphoplasty

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces.

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.

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

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 became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reaction-diffusion systems with chemical-biological applications, evolutionary free boundary problems of parabolic type or for Navier-Stokes equations, and a variational approach to evolution problems for the Ginzburg-Landau functional.

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view.The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

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 the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. 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. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the well-posedness theory of linear transport equations with irregular coefficients, and the study of the BV-like structure of bounded entropy solutions to multi-dimensional scalar conservation laws.The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory.

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.

The book contains a selection of 43 scientific papers by the great mathematician Ennio De Giorgi (1928-1996), which display the broad range of his achievements and his entire intellectual career as a problem solver and as a proponent of deep and ambitious mathematical theories. All papers are written in English and 17 of them appear also in their original Italian version in order to give an impression of De Giorgi’s original style. The editors also provide a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert’s 19th problem to the theory of perimeter and minimal surfaces, the theory of G-convergence and the foundations of mathematics.

This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. The book originates from lectures by L. Ambrosio at the ETH Zurich in Fall 2001 and contains new results.

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 and 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.

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 isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.