Variational Techniques For Elliptic Partial Differential Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Variational Techniques For Elliptic Partial Differential Equations PDF full book. Access full book title Variational Techniques For Elliptic Partial Differential Equations.
Author | : Francisco J. Sayas |
Publisher | : CRC Press |
Total Pages | : 492 |
Release | : 2019-01-16 |
Genre | : Mathematics |
ISBN | : 0429016204 |
Download Variational Techniques for Elliptic Partial Differential Equations Book in PDF, ePub and Kindle
Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics
Author | : Vicentiu D. Radulescu |
Publisher | : Hindawi Publishing Corporation |
Total Pages | : 205 |
Release | : 2008 |
Genre | : Differential equations, Elliptic |
ISBN | : 9774540395 |
Download Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations Book in PDF, ePub and Kindle
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.
Author | : Qing Han |
Publisher | : American Mathematical Soc. |
Total Pages | : 161 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821853139 |
Download Elliptic Partial Differential Equations Book in PDF, ePub and Kindle
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Author | : M. A. Lavrent’ev |
Publisher | : Courier Dover Publications |
Total Pages | : 160 |
Release | : 2016-01-14 |
Genre | : Mathematics |
ISBN | : 0486160289 |
Download Variational Methods for Boundary Value Problems for Systems of Elliptic Equations Book in PDF, ePub and Kindle
Famous monograph by a distinguished mathematician presents an innovative approach to classical boundary value problems. The treatment employs the basic scheme first suggested by Hilbert and developed by Tonnelli. 1963 edition.
Author | : Wolfgang Hackbusch |
Publisher | : Springer |
Total Pages | : 455 |
Release | : 2017-06-01 |
Genre | : Mathematics |
ISBN | : 3662549611 |
Download Elliptic Differential Equations Book in PDF, ePub and Kindle
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Author | : W. Hackbusch |
Publisher | : Springer Science & Business Media |
Total Pages | : 334 |
Release | : 1992 |
Genre | : Language Arts & Disciplines |
ISBN | : 9783540548225 |
Download Elliptic Differential Equations Book in PDF, ePub and Kindle
Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Author | : Françoise Demengel |
Publisher | : Springer Science & Business Media |
Total Pages | : 480 |
Release | : 2012-01-24 |
Genre | : Mathematics |
ISBN | : 1447128079 |
Download Functional Spaces for the Theory of Elliptic Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Marino Badiale |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2010-12-07 |
Genre | : Mathematics |
ISBN | : 0857292277 |
Download Semilinear Elliptic Equations for Beginners Book in PDF, ePub and Kindle
Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.
Author | : Mario Girardi |
Publisher | : |
Total Pages | : 208 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : |
Download Progress in Variational Methods in Hamiltonian Systems and Elliptic Equations Book in PDF, ePub and Kindle
This research note gives a comprehensive account of the use of variational methods in the study of Hamiltonian systems and elliptic equations.
Author | : Jan Malý |
Publisher | : American Mathematical Soc. |
Total Pages | : 309 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821803352 |
Download Fine Regularity of Solutions of Elliptic Partial Differential Equations Book in PDF, ePub and Kindle
The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.