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 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...
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 ...
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, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on 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...
This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz...
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...
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...
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...
Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biologica...
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. 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. Readers should have basic knowledge of PDE and measure theory.
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. This volume provides an up-...
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. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
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 pro...
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampere 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.
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-A...
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...
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 ach...
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 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...
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...
There have been important developments in materials and therapies for the treatment of spinal conditions. Biomaterials for spinal surgery summarises t...
