Maximum Principles And Geometric Applications PDF Download
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Author | : Luis J. Alías |
Publisher | : Springer |
Total Pages | : 594 |
Release | : 2016-02-13 |
Genre | : Mathematics |
ISBN | : 3319243373 |
Download Maximum Principles and Geometric Applications Book in PDF, ePub and Kindle
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 | : Stefano Pigola |
Publisher | : American Mathematical Soc. |
Total Pages | : 118 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821836390 |
Download Maximum Principles on Riemannian Manifolds and Applications Book in PDF, ePub and Kindle
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 |
Total Pages | : 236 |
Release | : 2007-12-23 |
Genre | : Mathematics |
ISBN | : 3764381450 |
Download The Maximum Principle Book in PDF, ePub and Kindle
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 | : Sperb |
Publisher | : Academic Press |
Total Pages | : 223 |
Release | : 1981-07-28 |
Genre | : Computers |
ISBN | : 0080956645 |
Download Maximum Principles and Their Applications Book in PDF, ePub and Kindle
Maximum Principles and Their Applications
Author | : Mathematical Sciences Research Institute (Berkeley, Calif.). |
Publisher | : |
Total Pages | : 9 |
Release | : 1989 |
Genre | : |
ISBN | : |
Download A Generalized Maximum Principle and Its Applications in Geometry Book in PDF, ePub and Kindle
Author | : M. J. Sewell |
Publisher | : CUP Archive |
Total Pages | : 496 |
Release | : 1987-12-17 |
Genre | : Mathematics |
ISBN | : 9780521332446 |
Download Maximum and Minimum Principles Book in PDF, ePub and Kindle
This book provides a unified account of the theory required to establish upper and lower bounds.
Author | : Serena Dipierro |
Publisher | : Springer |
Total Pages | : 502 |
Release | : 2019-07-12 |
Genre | : Mathematics |
ISBN | : 303018921X |
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.
Author | : Bruno Bianchini |
Publisher | : Springer Nature |
Total Pages | : 291 |
Release | : 2021-01-18 |
Genre | : Mathematics |
ISBN | : 3030627047 |
Download Geometric Analysis of Quasilinear Inequalities on Complete Manifolds Book in PDF, ePub and Kindle
This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Author | : Stefano Biagi |
Publisher | : World Scientific |
Total Pages | : 450 |
Release | : 2018-12-05 |
Genre | : Mathematics |
ISBN | : 9813276630 |
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:
Author | : Michel Boileau |
Publisher | : Springer |
Total Pages | : 136 |
Release | : 2016-09-09 |
Genre | : Mathematics |
ISBN | : 3319423517 |
Download Ricci Flow and Geometric Applications Book in PDF, ePub and Kindle
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.