Function Spaces and Partial Differential Equations

Author: Ali Taheri
Publisher: Oxford University Press, USA
ISBN: 9780198733133
Release Date: 2015
Genre: Differential equations, Partial

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Topics on Analysis in Metric Spaces

Author: Luigi Ambrosio
Publisher: Oxford University Press on Demand
ISBN: 0198529384
Release Date: 2004
Genre: Mathematics

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 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 the 'cavalieri' formula as the definition of the integral. Based on lecture notes from 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.

Functional Analysis Sobolev Spaces and Partial Differential Equations

Author: Haim Brezis
Publisher: Springer Science & Business Media
ISBN: 9780387709147
Release Date: 2010-11-02
Genre: Mathematics

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

An Introduction to Semilinear Evolution Equations

Author: Thierry Cazenave
Publisher: Oxford University Press on Demand
ISBN: 019850277X
Release Date: 1998
Genre: Mathematics

This book presents an upper level text on semilinear evolutionary partial differential equations aimed at the graduate and postgraduate level. Cazenave and Haraux present in a self-contained way, the typical basic properties of solutions to semi-linear evolutionary partial differential equations, with special emphasis on global properties. The main objective of this book is to provide a didactic approach to the subject , and the main readership will be graduate students in mathematical analysis, as well as professional applied mathematicians.

Mathematical Tools for Physicists

Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 9783527684274
Release Date: 2014-11-05
Genre: Science

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Function Spaces and Partial Differential Equations

Author: Ali Taheri
Publisher: Oxford University Press
ISBN: 9780191047855
Release Date: 2015-07-30
Genre: Mathematics

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Graph Theory As I Have Known It

Author: W. T. Tutte
Publisher: OUP Oxford
ISBN: 9780191637780
Release Date: 1998-06-11
Genre: Mathematics

Graph Theory as I Have Known It provides a unique introduction to graph theory by one of the founding fathers, and will appeal to anyone interested in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers. The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as combinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided. William Tutte (1917-2002) studied at Cambridge where his fascination for mathematical puzzles brought him into contact with like-minded undergraduates, together becoming known as the 'Trinity four', the founders of modern graph theory. His notable problem-solving skills meant he was brought to Bletchley Park during World War Two. Key in the enemy codebreaking efforts, he cracked the Lorenz cipher for which the Colossus machine was built, making his contribution comparable to Alan Turing's codebreaking for Enigma. Following his incredible war effort Tutte returned to academia and became a fellow of the Royal Society in Britain and Canada, finishing his career as Distinguished Professor Emeritus at the University of Waterloo, Ontario.

Perfect Incompressible Fluids

Author: Jean-Yves Chemin
Publisher: Oxford University Press
ISBN: 0198503970
Release Date: 1998
Genre: Mathematics

The aim of this book is to offer a direct and self-contained access to some of the new or recent results in fluid mechanics. It gives an authoritative account on the theory of the Euler equations describing a perfect incompressible fluid. First of all, the text derives the Euler equations from a variational principle, and recalls the relations on vorticity and pressure. Various weak formulations are proposed. The book then presents the tools of analysis necessary for their study:Littlewood-Paley theory, action of Fourier multipliers on L spaces, and partial differential calculus. These techniques are then used to prove various recent results concerning vortext patches or sheets, essentially the persistence of the smoothness of the boundary of a vortex patch, even if that smoothness allows singular points, as well as the existence of weak solutions of the vorticity sheet type. The text also presents properties of microlocal (analytic or Gevrey) regularity of thesolutions of Euler equations, and provides links of such properties to the smoothness in time of the flow of the solution vector field.

Gamma convergence for Beginners

Author: Andrea Braides
Publisher: Clarendon Press
ISBN: 9780198507840
Release Date: 2002
Genre: Mathematics

This is a handbook of Gamma-convergence, which is a theoretical tool to study problems in applied mathematics where varying parameters are present, with many applications that range from mechanics to computer vision.