Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds
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Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds
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Author : Bruno Bianchini
language : en
Publisher: Springer Nature
Release Date : 2021-01-18
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds written by Bruno Bianchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.
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.
Geometric And Functional Inequalities And Recent Topics In Nonlinear Pdes
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Author : Emanuel Indrei
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-09
Geometric And Functional Inequalities And Recent Topics In Nonlinear Pdes written by Emanuel Indrei and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-09 with Mathematics categories.
This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.
The Ab Program In Geometric Analysis Sharp Sobolev Inequalities And Related Problems
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Author : Olivier Druet
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
The Ab Program In Geometric Analysis Sharp Sobolev Inequalities And Related Problems written by Olivier Druet and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.
Nonlinear Analysis On Manifolds Sobolev Spaces And Inequalities
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Author : Emmanuel Hebey
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-10-27
Nonlinear Analysis On Manifolds Sobolev Spaces And Inequalities written by Emmanuel Hebey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-27 with Mathematics categories.
This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. ``Several surprising phenomena appear when studying Sobolev spaces on manifolds,'' according to the author. ``Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.'' The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.
Geometric Analysis
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Author : Jingyi Chen
language : en
Publisher: Springer Nature
Release Date : 2020-04-10
Geometric Analysis written by Jingyi Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-10 with Mathematics categories.
This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.
Convex Analysis And Nonlinear Geometric Elliptic Equations
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Author : Ilya J. Bakelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Convex Analysis And Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
On Some Aspects Of Oscillation Theory And Geometry
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Author : Bruno Bianchini
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-23
On Some Aspects Of Oscillation Theory And Geometry written by Bruno Bianchini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Mathematics categories.
The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.
Analysis And Partial Differential Equations On Manifolds Fractals And Graphs
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Author : Alexander Grigor'yan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-01-18
Analysis And Partial Differential Equations On Manifolds Fractals And Graphs written by Alexander Grigor'yan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Variational Principles In Mathematical Physics Geometry And Economics
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Author : Alexandru Kristály
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-19
Variational Principles In Mathematical Physics Geometry And Economics written by Alexandru Kristály and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Mathematics categories.
A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.
Analysis Manifolds And Physics Revised Edition
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: Gulf Professional Publishing
Release Date : 1982
Analysis Manifolds And Physics Revised Edition written by Yvonne Choquet-Bruhat and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.