| 书目名称 | Geometric Analysis of Quasilinear Inequalities on Complete Manifolds | | 副标题 | Maximum and Compact | | 编辑 | Bruno Bianchini,Luciano Mari,Marco Rigoli | | 视频video | | | 概述 | Investigates the validity of strong maximum principles, compact support principles and Liouville type theorems.Aims to give a unified view of recent results in the literature | | 丛书名称 | Frontiers in Mathematics | | 图书封面 |  | | 描述 | 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 improv | | 出版日期 | Book 2021 | | 关键词 | Coercive Differential Inequalities; Compact Support Principle; Liouville Properties; Maximum Principle; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-62704-1 | | isbn_softcover | 978-3-030-62703-4 | | isbn_ebook | 978-3-030-62704-1Series ISSN 1660-8046 Series E-ISSN 1660-8054 | | issn_series | 1660-8046 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 17:44:17
