Maximum Principles And Geometric Applications
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Maximum Principles and Geometric Applications
Author | : Luis J. Alías,Paolo Mastrolia,Marco Rigoli |
Publsiher | : Springer |
Total Pages | : 570 |
Release | : 2016-02-13 |
Genre | : Mathematics |
ISBN | : 9783319243375 |
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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.
Maximum Principles on Riemannian Manifolds and Applications
Author | : Stefano Pigola,Marco Rigoli,Alberto Giulio Setti |
Publsiher | : American Mathematical Soc. |
Total Pages | : 99 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 9780821836392 |
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The aim of this paper is 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 recently obtained by the authors. Applications are given to a number of geometrical problems in the setting of complete Riemannian manifolds, under assumptions either on the curvature or on the volume growth of geodesic balls.
The Maximum Principle
Author | : Patrizia Pucci,J. B. Serrin |
Publsiher | : Springer Science & Business Media |
Total Pages | : 236 |
Release | : 2007-12-23 |
Genre | : Mathematics |
ISBN | : 9783764381455 |
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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.
Maximum Principles and Their Applications
Author | : Sperb |
Publsiher | : Academic Press |
Total Pages | : 223 |
Release | : 1981-07-28 |
Genre | : Computers |
ISBN | : 9780080956640 |
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Maximum Principles and Their Applications
Maximum and Minimum Principles
Author | : M. J. Sewell |
Publsiher | : CUP Archive |
Total Pages | : 496 |
Release | : 1987-12-17 |
Genre | : Mathematics |
ISBN | : 0521332443 |
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This book provides a unified account of the theory required to establish upper and lower bounds.
Maximum Principles in Differential Equations
Author | : Murray H. Protter,Hans F. Weinberger |
Publsiher | : Springer Science & Business Media |
Total Pages | : 271 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461252825 |
Download Maximum Principles in Differential Equations Book in PDF, Epub and Kindle
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.
An Introduction To The Geometrical Analysis Of Vector Fields With Applications To Maximum Principles And Lie Groups
Author | : Stefano Biagi,Andrea Bonfiglioli |
Publsiher | : World Scientific |
Total Pages | : 450 |
Release | : 2018-12-05 |
Genre | : Mathematics |
ISBN | : 9789813276635 |
Download An Introduction To The Geometrical Analysis Of Vector Fields With Applications To Maximum Principles And Lie Groups Book in PDF, Epub and Kindle
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
Contemporary Research in Elliptic PDEs and Related Topics
Author | : Serena Dipierro |
Publsiher | : Springer |
Total Pages | : 502 |
Release | : 2019-07-12 |
Genre | : Mathematics |
ISBN | : 9783030189211 |
Download Contemporary Research in Elliptic PDEs and Related Topics Book in PDF, Epub and Kindle
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.