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.
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
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.
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.
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.
Download or read book Maximum and Minimum Principles written by M. J. Sewell and published by CUP Archive. This book was released on 1987-12-17 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified account of the theory required to establish upper and lower bounds.
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.
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.
Download or read book Maximum Principles on Riemannian Manifolds and Applications written by Stefano Pigola and published by American Mathematical Soc.. This book was released on 2005 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
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.
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
Download or read book Maximum Principles and Their Applications written by and published by . This book was released on 1981 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Theory of Optimal Processes written by L.S. Pontryagin and published by Routledge. This book was released on 2018-05-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.
Download or read book The Principles of Mathematics written by Bertrand Russell and published by W. W. Norton & Company. This book was released on 1996 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.
Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Download or read book The Fractional Laplacian written by Wenxiong Chen and published by World Scientific. This book was released on 2020-06-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.
Download or read book Maximum Principle for Non hyperbolic Equations written by Jaak Peetre and published by . This book was released on 1962 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
