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Maximum Principles In Differential Equations
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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 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 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 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 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.
Book Synopsis Maximum Principles in Differential Equations and Their Applications by : Michael J. Mears
Download or read book Maximum Principles in Differential Equations and Their Applications written by Michael J. Mears and published by . This book was released on with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Maximum Principles and Eigenvalue Problems in Partial Differential Equations by : P. W. Schaefer
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:
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 Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems by : Gershon Kresin
Download or read book Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems written by Gershon Kresin and published by American Mathematical Soc.. This book was released on 2012-08-15 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
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 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Principles and Their Applications
Book Synopsis Order Structure And Topological Methods In Nonlinear Partial Differential Equations: Vol. 1: Maximum Principles And Applications by : Yihong Du
Download or read book Order Structure And Topological Methods In Nonlinear Partial Differential Equations: Vol. 1: Maximum Principles And Applications written by Yihong Du and published by World Scientific. This book was released on 2006-01-12 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 Maximum Principles for P-Functions in Elliptic Partial Differential Equations by : Edward Caston Nichols
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:
Book Synopsis The Action Principle and Partial Differential Equations. (AM-146), Volume 146 by : Demetrios Christodoulou
Download or read book The Action Principle and Partial Differential Equations. (AM-146), Volume 146 written by Demetrios Christodoulou and published by Princeton University Press. This book was released on 2016-03-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media.
Book Synopsis The One-dimensional Maximum Principles in Differential Equations with Applications to Boundary Value and Initial Value Problems by : Dwight W. Snuffer
Download or read book The One-dimensional Maximum Principles in Differential Equations with Applications to Boundary Value and Initial Value Problems written by Dwight W. Snuffer and published by . This book was released on 1972 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Principles, Gradient Estimates, and Weak Solutions for Partial Differential Equations of Elliptic and Parabolic Type by : William Israel Bertiger
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:
