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The Maximum Principle
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Book Synopsis The Maximum Principle by : Patrizia Pucci
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.
Book Synopsis Maximum Principles and Geometric Applications by : Luis J. Alías
Download or read book Maximum Principles and Geometric Applications written by Luis J. Alías and published by Springer. This book was released on 2016-02-13 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on. Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.
Book Synopsis Income, Wealth, and the Maximum Principle by : Martin L. Weitzman
Download or read book Income, Wealth, and the Maximum Principle written by Martin L. Weitzman and published by Harvard University Press. This book was released on 2009-07-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact and original exposition of optimal control theory and applications is designed for graduate and advanced undergraduate students in economics. It presents a new elementary yet rigorous proof of the maximum principle and a new way of applying the principle that will enable students to solve any one-dimensional problem routinely. Its unified framework illuminates many famous economic examples and models. This work also emphasizes the connection between optimal control theory and the classical themes of capital theory. It offers a fresh approach to fundamental questions such as: What is income? How should it be measured? What is its relation to wealth? The book will be valuable to students who want to formulate and solve dynamic allocation problems. It will also be of interest to any economist who wants to understand results of the latest research on the relationship between comprehensive income accounting and wealth or welfare.
Book Synopsis An Introduction to Maximum Principles and Symmetry in Elliptic Problems by : L. E. Fraenkel
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 :Vladimir G. Boltyanski Publisher :Springer Science & Business Media ISBN 13 :0817681523 Total Pages :440 pages Book Rating :4.8/5 (176 download)
Book Synopsis The Robust Maximum Principle by : Vladimir G. Boltyanski
Download or read book The Robust Maximum Principle written by Vladimir G. Boltyanski and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering some of the key areas of optimal control theory (OCT), a rapidly expanding field, the authors use new methods to set out a version of OCT’s more refined ‘maximum principle.’ The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games. This book explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.
Book Synopsis Order Structure and Topological Methods in Nonlinear Partial Differential Equations by : Yihong Du
Download or read book Order Structure and Topological Methods in Nonlinear Partial Differential Equations written by Yihong Du and published by World Scientific. This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
Book Synopsis Elliptic Partial Differential Equations of Second Order by : D. Gilbarg
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.
Book Synopsis Maximum Principles for the Hill's Equation by : Alberto Cabada
Download or read book Maximum Principles for the Hill's Equation written by Alberto Cabada and published by Academic Press. This book was released on 2017-10-27 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,...) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included. - Evaluates classical topics in the Hill's equation that are crucial for understanding modern physical models and non-linear applications - Describes explicit and effective conditions on maximum and anti-maximum principles - Collates information from disparate sources in one self-contained volume, with extensive referencing throughout
Book Synopsis Fractional Differential Equations by : Anatoly Kochubei
Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Book Synopsis Maximum Principles in Differential Equations by : Murray H. Protter
Download or read book Maximum Principles in Differential Equations written by Murray H. Protter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Principles are central to the theory and applications of second-order partial differential equations and systems. This self-contained text establishes the fundamental principles and provides a variety of applications.
Book Synopsis Maximum Principles and Their Applications by : Sperb
Download or read book Maximum Principles and Their Applications written by Sperb and published by Academic Press. This book was released on 1981-07-28 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Principles and Their Applications
Book Synopsis Elliptic Partial Differential Equations by : Qing Han
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.
Book Synopsis Stable Solutions of Elliptic Partial Differential Equations by : Louis Dupaigne
Download or read book Stable Solutions of Elliptic Partial Differential Equations written by Louis Dupaigne and published by CRC Press. This book was released on 2011-03-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Book Synopsis Maximum Principles in Differential Equations by : Murray H. Protter
Download or read book Maximum Principles in Differential Equations written by Murray H. Protter and published by . This book was released on 1967 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control Theory by : Suresh P. Sethi
Download or read book Optimal Control Theory written by Suresh P. Sethi and published by Taylor & Francis US. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.
Book Synopsis Mathematical Control Theory by : Jerzy Zabczyk
Download or read book Mathematical Control Theory written by Jerzy Zabczyk and published by Springer Science & Business Media. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.
