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Author : Edward Caston Nichols
Publisher :
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.:/5 (15 download)
Download or read book Maximum Principles for P-Functions in Elliptic Partial Differential Equations written by Edward Caston Nichols and published by . This book was released on 1986 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Patrizia Pucci
Publisher : Springer Science & Business Media
ISBN 13 : 3764381450
Total Pages : 240 pages
Book Rating : 4.7/5 (643 download)
Download or read book The Maximum Principle written by Patrizia Pucci and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
Author : Qing Han
Publisher : American Mathematical Soc.
ISBN 13 : 0821853139
Total Pages : 161 pages
Book Rating : 4.8/5 (218 download)
Download or read book Elliptic Partial Differential Equations written by Qing Han and published by American Mathematical Soc.. This book was released on 2011 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : L. E. Fraenkel
Publisher : Cambridge University Press
ISBN 13 : 0521461952
Total Pages : 352 pages
Book Rating : 4.5/5 (214 download)
Download or read book An Introduction to Maximum Principles and Symmetry in Elliptic Problems written by L. E. Fraenkel and published by Cambridge University Press. This book was released on 2000-02-25 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints.
Author : David Gilbarg
Publisher : Springer Science & Business Media
ISBN 13 : 9783540411604
Total Pages : 544 pages
Book Rating : 4.4/5 (116 download)
Download or read book Elliptic Partial Differential Equations of Second Order written by David Gilbarg and published by Springer Science & Business Media. This book was released on 2001-01-12 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.
Author : William Israel Bertiger
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (34 download)
Download or read book Maximum Principles, Gradient Estimates, and Weak Solutions for Partial Differential Equations of Elliptic and Parabolic Type written by William Israel Bertiger and published by . This book was released on 1976 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. W. Schaefer
Publisher : Longman
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.:/5 (5 download)
Download or read book Maximum Principles and Eigenvalue Problems in Partial Differential Equations written by P. W. Schaefer and published by Longman. This book was released on 1988 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. R. Garabedian
Publisher : American Mathematical Society
ISBN 13 : 1470475057
Total Pages : 686 pages
Book Rating : 4.4/5 (74 download)
Download or read book Partial Differential Equations written by P. R. Garabedian and published by American Mathematical Society. This book was released on 2023-10-19 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a review of the original edition: This book is primarily a text for a graduate course in partial differential equations, although the later chapters are devoted to special topics not ordinarily covered in books in this field … [T]he author has made use of an interesting combination of classical and modern analysis in his proofs … Because of the author's emphasis on constructive methods for solving problems which are of physical interest, his book will likely be as welcome to the engineer and the physicist as to the mathematician … The author and publisher are to be complimented on the general appearance of the book. —Mathematical Reviews This book is a gem. It fills the gap between the standard introductory material on PDEs that an undergraduate is likely to encounter after a good ODE course (separation of variables, the basics of the second-order equations from mathematical physics) and the advanced methods (such as Sobolev spaces and fixed point theorems) that one finds in modern books. Although this is not designed as a textbook for applied mathematics, the approach is strongly informed by applications. For instance, there are many existence and uniqueness results, but they are usually approached via very concrete techniques. The text contains the standard topics that one expects in an intermediate PDE course: the Dirichlet and Neumann problems, Cauchy's problem, characteristics, the fundamental solution, PDEs in the complex domain, plus a chapter on finite differences, on nonlinear fluid mechanics, and another on integral equations. It is an excellent text for advanced undergraduates or beginning graduate students in mathematics or neighboring fields, such as engineering and physics, where PDEs play a central role.
Author : D. Gilbarg
Publisher : Springer Science & Business Media
ISBN 13 : 364296379X
Total Pages : 409 pages
Book Rating : 4.6/5 (429 download)
Download or read book Elliptic Partial Differential Equations of Second Order written by D. Gilbarg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended as an essentially self contained exposition of portions of the theory of second order quasilinear elliptic partial differential equations, with emphasis on the Dirichlet problem in bounded domains. It grew out of lecture notes for graduate courses by the authors at Stanford University, the final material extending well beyond the scope of these courses. By including preparatory chapters on topics such as potential theory and functional analysis, we have attempted to make the work accessible to a broad spectrum of readers. Above all, we hope the readers of this book will gain an appreciation of the multitude of ingenious barehanded techniques that have been developed in the study of elliptic equations and have become part of the repertoire of analysis. Many individuals have assisted us during the evolution of this work over the past several years. In particular, we are grateful for the valuable discussions with L. M. Simon and his contributions in Sections 15.4 to 15.8; for the helpful comments and corrections of J. M. Cross, A. S. Geue, J. Nash, P. Trudinger and B. Turkington; for the contributions of G. Williams in Section 10.5 and of A. S. Geue in Section 10.6; and for the impeccably typed manuscript which resulted from the dedicated efforts oflsolde Field at Stanford and Anna Zalucki at Canberra. The research of the authors connected with this volume was supported in part by the National Science Foundation.
Author : Abdelmoujib Benkirane
Publisher : CRC Press
ISBN 13 : 9780203910108
Total Pages : 316 pages
Book Rating : 4.9/5 (11 download)
Download or read book Partial Differential Equations written by Abdelmoujib Benkirane and published by CRC Press. This book was released on 2002-05-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This impressive compilation of the material presented at the International Conference on Partial Differential Equations held in Fez, Morocco, represents an integrated discussion of all major topics in the area of partial differential equations--highlighting recent progress and new trends for real-world applications.
Author : Françoise Demengel
Publisher : Springer Science & Business Media
ISBN 13 : 1447128079
Total Pages : 480 pages
Book Rating : 4.4/5 (471 download)
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.
Author : Sajan K. Samuel
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)
Download or read book On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems written by Sajan K. Samuel and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "One of the most important and useful tools used in the study of partial differential equations is the maximum principle. This principle is a natural extension to higher dimensions of an elementary fact of calculus: any function, which satisfies the inequality f′′ > 0 on an interval [a,b], achieves its maximum at one of the endpoints of the interval. In this context, we say that the solution to the differential inequality f′′ > 0 satisfies a maximum principle. In this thesis we will discuss the maximum principles for partial differential equations and their applications. More precisely, we will show how one may employ the maximum principles to obtain information about uniqueness, approximation, boundedness, convexity, symmetry or asymptotic behavior of solutions, without any explicit knowledge of the solutions themselves. The thesis will be organized in two main parts. The purpose of the first part is to briefly introduce in Chapter 1 the terminology and the main tools to be used throughout this thesis. We will start by introducing the second order linear differential operators of elliptic and parabolic type. Then, we will develop the first and second maximum principles of E. Hopf for elliptic equations, respectively the maximum principles of L. Nirenberg and A. Friedman for parabolic equations. Next, in the second part, namely in Chapter 2 and 3, we will introduce various P-functions, which are nothing else than appropriate functional combinations of the solutions and their derivatives, and derive new maximum principles for such functionals. Moreover, we will show how to employ these new maximum principles to get isoperimetric inequalities, symmetry results and convexity results in the elliptic case (Chapter 2), respectively spatial and temporal asymptotic behavior of solutions, in the parabolic case (Chapter 3)."--Abstract.
Author : A Alvino
Publisher : CRC Press
ISBN 13 : 9780582259706
Total Pages : 236 pages
Book Rating : 4.2/5 (597 download)
Download or read book Progress in Elliptic and Parabolic Partial Differential Equations written by A Alvino and published by CRC Press. This book was released on 1996-05-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note collects reports of the invited plenary addresses given during the conference Elliptic and Parabolic Partial Differential Equations and Applications held in Capri, Italy, 19-23 September 1994. The conference was devoted to new developments in partial differential equations of elliptic and parabolic type and to their applications in various fields.
Author : Lipman Bers
Publisher : American Mathematical Soc.
ISBN 13 : 0821800493
Total Pages : 370 pages
Book Rating : 4.8/5 (218 download)
Download or read book Partial Differential Equations written by Lipman Bers and published by American Mathematical Soc.. This book was released on 1964 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divided in two main parts, this title contains an assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. Suitable for graduate students and researchers interested in partial differential equations, it also includes a discussion of some quasi-linear elliptic equations.
Author : Svetlin G. Georgiev
Publisher : CRC Press
ISBN 13 : 100097006X
Total Pages : 302 pages
Book Rating : 4.0/5 (9 download)
Download or read book Multiplicative Partial Differential Equations written by Svetlin G. Georgiev and published by CRC Press. This book was released on 2023-10-30 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiplicative Partial Differential Equations presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The author’s aim is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text material of this book is presented in a highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. Features Includes new classification and canonical forms of second-order MPDEs Proposes a new technique to solving the multiplicative wave equation such as the method of separation of variables and the energy method The proposed technique in the book can be used to give the basic properties of multiplicative elliptic problems, fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, mean-value formulas, strong principle of maximum, multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, and theorems of Liouville and Harnack
Author : Cristian -. Paul Danet
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659405563
Total Pages : 100 pages
Book Rating : 4.4/5 (55 download)
Download or read book The Classical Maximum Principle. Some Extensions and Applications written by Cristian -. Paul Danet and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maximum principle is one of the most useful and best known tools employed in the study of partial differential equations. The maximum principle enables us to obtain information about uniqueness, approximation, boundedness and symmetry of the solution, bounds for the first eigenvalue, quantities of physical interest, necessary conditions of solvability for some boundary value problems, etc. The book is divided into two parts. Part I contains two chapters and presents the classical maximum principle for linear equations, some of its direct extensions for nonlinear equations and their applications. Part II of this book is divided into three chapters and is devoted to the P function method and its applications. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in elliptic partial differential equations.
Author : David Gilbarg
Publisher :
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.F/5 ( download)
Download or read book Lectures on Elliptic Partial Differential Equations written by David Gilbarg and published by . This book was released on 1958 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
