Maximum Principles and Their Applications PDF Download

Author: Sperb
Publisher: Academic Press
ISBN: 0080956645
Category : Computers
Languages : en
Pages : 235

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Maximum Principles and Their Applications

Author: Luis J. Alías
Publisher: Springer
ISBN: 3319243373
Category : Mathematics
Languages : en
Pages : 594

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Book Description
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
ISBN: 9812566244
Category : Mathematics
Languages : en
Pages : 202

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Book Description
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: Alberto Cabada
Publisher: Academic Press
ISBN: 0128041269
Category : Mathematics
Languages : en
Pages : 254

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Book Description
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: Murray H. Protter
Publisher: Springer Science & Business Media
ISBN: 1461252822
Category : Mathematics
Languages : en
Pages : 271

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Book Description
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: M. J. Sewell
Publisher: CUP Archive
ISBN: 9780521332446
Category : Mathematics
Languages : en
Pages : 496

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Book Description
This book provides a unified account of the theory required to establish upper and lower bounds.

Author: Stefano Pigola
Publisher: American Mathematical Soc.
ISBN: 0821836390
Category : Mathematics
Languages : en
Pages : 118

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Book Description
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: Patrizia Pucci
Publisher: Springer Science & Business Media
ISBN: 3764381450
Category : Mathematics
Languages : en
Pages : 240

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Book Description
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
ISBN: 3110571668
Category : Mathematics
Languages : en
Pages : 528

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Book Description
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: Bennett Chow
Publisher: American Mathematical Soc.
ISBN: 0821844296
Category : Global differential geometry
Languages : en
Pages : 489

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