Maximum Principles In Differential Equations
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Maximum Principles In Differential Equations
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Author : Murray H. Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Maximum Principles In Differential Equations written by Murray H. Protter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Maximum Principle
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Author : Patrizia Pucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-23
The Maximum Principle written by Patrizia Pucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-23 with Mathematics categories.
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.
Maximum Principles In Differential Equations
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Author : Murray H. Protter
language : en
Publisher:
Release Date : 1984-01-01
Maximum Principles In Differential Equations written by Murray H. Protter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Differential equations, Partial categories.
Maximum principles are central to the theory and applications of second-order partial differential equations and systems. This text establishes the fundamental principles and provides a variety of applications.
Maximum Principles And Geometric Applications
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Author : Luis J. Alías
language : en
Publisher: Springer
Release Date : 2019-03-21
Maximum Principles And Geometric Applications written by Luis J. Alías and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-21 with Mathematics categories.
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.
Elliptic Partial Differential Equations Of Second Order
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Author : D. Gilbarg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elliptic Partial Differential Equations Of Second Order written by D. Gilbarg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Partial Differential Equations And Applications
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Author : Giorgio Talenti
language : en
Publisher: CRC Press
Release Date : 1996-01-16
Partial Differential Equations And Applications written by Giorgio Talenti and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-16 with Mathematics categories.
Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.
Nonoscillation Theory Of Functional Differential Equations With Applications
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Nonoscillation Theory Of Functional Differential Equations With Applications written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.
Essential Partial Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer
Release Date : 2015-09-24
Essential Partial Differential Equations written by David F. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Second Order Parabolic Differential Equations
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Author : Gary M. Lieberman
language : en
Publisher: World Scientific
Release Date : 1996
Second Order Parabolic Differential Equations written by Gary M. Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.