Download or read book Distributions written by Pulin Kumar Bhattacharyya and published by Walter de Gruyter. This book was released on 2012-05-29 with total page 871 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc., who were interested in studying the problems of mathematical physics in general and their approximate solutions on computer in particular. Almost all topics which will be essential for the study of Sobolev spaces and their applications in the elliptic boundary value problems and their finite element approximations are presented. Also many additional topics of interests for specific applied disciplines and engineering, for example, elementary solutions, derivatives of discontinuous functions of several variables, delta-convergent sequences of functions, Fourier series of distributions, convolution system of equations etc. have been included along with many interesting examples.
Download or read book An Introduction to Sobolev Spaces and Interpolation Spaces written by Luc Tartar and published by Springer Science & Business Media. This book was released on 2007-05-26 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
Download or read book Fourier Analysis and Partial Differential Equations written by Iorio Júnior Iorio Jr. and published by Cambridge University Press. This book was released on 2001-03-15 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.
Download or read book Distributions Sobolev Spaces Elliptic Equations written by Dorothee Haroske and published by European Mathematical Society. This book was released on 2007 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.
Download or read book A First Course in Sobolev Spaces written by Giovanni Leoni and published by American Mathematical Soc.. This book was released on 2009 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables. The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces. The book contains over 200 exercises.
Download or read book Finite Elements I written by Alexandre Ern and published by Springer Nature. This book was released on 2021-03-22 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
Download or read book Problems on Partial Differential Equations written by Maciej Borodzik and published by Springer. This book was released on 2019-05-07 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and Sobolev spaces. In numerous problems, the student is asked to prove a given statement, e.g. to show the existence of a solution to a certain PDE. Usually there is no closed-formula answer available, which is why there is no answer section, although helpful hints are often provided. This textbook offers a valuable asset for students and educators alike. As it adopts a perspective on PDEs that is neither too theoretical nor too practical, it represents the perfect companion to a broad spectrum of courses.
Download or read book Functional Analysis Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Weakly Differentiable Functions written by William P. Ziemer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "weakly differentiable functions" in the title refers to those inte n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV func tions), have undergone considerable development during the past 20 years. From this development a rather complete theory has emerged and thus has provided the main impetus for the writing of this book. Since these classes of functions play a significant role in many fields, such as approximation theory, calculus of variations, partial differential equations, and non-linear potential theory, it is hoped that this monograph will be of assistance to a wide range of graduate students and researchers in these and perhaps other related areas. Some of the material in Chapters 1-4 has been presented in a graduate course at Indiana University during the 1987-88 academic year, and I am indebted to the students and colleagues in attendance for their helpful comments and suggestions.
Download or read book Introduction to the Theory of Distributions written by F. G. Friedlander and published by Cambridge University Press. This book was released on 1998 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a classic graduate text on the theory of distributions.
Download or read book Distributions and Operators written by Gerd Grubb and published by Springer Science & Business Media. This book was released on 2008-10-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.
Download or read book A Guide to Distribution Theory and Fourier Transforms written by Robert S. Strichartz and published by World Scientific. This book was released on 2003 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Download or read book Theory of Distributions written by Svetlin G. Georgiev and published by Springer. This book was released on 2015-07-13 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
Download or read book Functional Spaces for the Theory of Elliptic Partial Differential Equations written by Françoise Demengel and published by Springer Science & Business Media. This book was released on 2012-01-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Download or read book Problems in Distributions and Partial Differential Equations written by C. Zuily and published by Elsevier. This book was released on 1988-04-01 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.
Download or read book Theory of Function Spaces IV written by Hans Triebel and published by Springer Nature. This book was released on 2020-01-23 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".
Download or read book Sobolev Spaces on Riemannian Manifolds written by Emmanuel Hebey and published by Springer. This book was released on 2006-11-14 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey's presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.
