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 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 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 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 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 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 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 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 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.
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 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 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 The Action Principle and Partial Differential Equations written by Demetrios Christodoulou and published by Princeton University Press. This book was released on 2000-01-17 with total page 332 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.
Download or read book Optimality Conditions Abnormal and Degenerate Problems written by Aram Arutyunov and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Download or read book Fractional Differential Equations written by Juan J. Nieto and published by MDPI. This book was released on 2019-11-19 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.
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.
Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
