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Author: Haim Brezis Publisher: Springer Science & Business Media ISBN: 0387709142 Category : Mathematics Languages : en Pages : 600
Book Description
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.
Author: Haim Brezis Publisher: Springer Science & Business Media ISBN: 0387709142 Category : Mathematics Languages : en Pages : 600
Book Description
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.
Author: Alberto Bressan Publisher: American Mathematical Soc. ISBN: 0821887718 Category : Mathematics Languages : en Pages : 265
Book Description
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Author: Friedrich Sauvigny Publisher: Springer Science & Business Media ISBN: 3540344624 Category : Mathematics Languages : en Pages : 401
Book Description
This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.
Author: Paul Sacks Publisher: Academic Press ISBN: 0128114576 Category : Mathematics Languages : en Pages : 322
Book Description
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. - Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas - Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations - Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
Author: Erik Koelink Publisher: Springer Science & Business Media ISBN: 3764376015 Category : Mathematics Languages : en Pages : 294
Book Description
Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis.
Author: Michael Renardy Publisher: Springer Science & Business Media ISBN: 0387216871 Category : Mathematics Languages : en Pages : 447
Book Description
Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.
Author: Françoise Demengel Publisher: Springer Science & Business Media ISBN: 1447128079 Category : Mathematics Languages : en Pages : 480
Book Description
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.
Author: Hans Wilhelm Alt Publisher: Springer ISBN: 1447172809 Category : Mathematics Languages : en Pages : 446
Book Description
This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.
Author: Mark Iosifovich Freidlin Publisher: Princeton University Press ISBN: 1400881595 Category : Mathematics Languages : en Pages : 557
Book Description
This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.
Author: Haim Brezis
Author: Haim Brezis
Author: Milan Miklavčič
Author: Alberto Bressan
Author: Friedrich Sauvigny
Author: Paul Sacks
Author: Erik Koelink
Author: Michael Renardy
Author: Françoise Demengel
Author: Hans Wilhelm Alt
Author: Mark Iosifovich Freidlin