Book Description
Maximum Principles and Their Applications
Author : Sperb
Publisher : Academic Press
Page : 235 pages
File Size : 29,18 MB
Release : 1981-07-28
Category : Computers
ISBN : 0080956645
Maximum Principles and Their Applications
Author : Luis J. Alías
Publisher : Springer
Page : 594 pages
File Size : 47,66 MB
Release : 2016-02-13
Category : Mathematics
ISBN : 3319243373
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.
Author : Yihong Du
Publisher : World Scientific
Page : 202 pages
File Size : 30,25 MB
Release : 2006
Category : Mathematics
ISBN : 9812566244
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.
Author : Stefano Pigola
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 30,9 MB
Release : 2005
Category : Mathematics
ISBN : 0821836390
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.
Author : Alberto Cabada
Publisher : Academic Press
Page : 254 pages
File Size : 12,70 MB
Release : 2017-10-27
Category : Mathematics
ISBN : 0128041269
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
Author : Patrizia Pucci
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 44,62 MB
Release : 2007-12-23
Category : Mathematics
ISBN : 3764381450
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.
Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
Page : 528 pages
File Size : 31,59 MB
Release : 2019-02-19
Category : Mathematics
ISBN : 3110571668
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.
Author : Murray H. Protter
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 30,4 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461252822
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.
Author : Bennett Chow
Publisher : American Mathematical Soc.
Page : 489 pages
File Size : 25,88 MB
Release : 2007
Category : Global differential geometry
ISBN : 0821844296
Author : Karmeshu
Publisher : Springer
Page : 300 pages
File Size : 25,55 MB
Release : 2012-10-01
Category : Technology & Engineering
ISBN : 3540362126
The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.