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Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds

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...

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Detalles Bibliográficos
Autores principales: Bianchini, Bruno, Mari, Luciano, Pucci, Patrizia, Rigoli, Marco
Lenguaje:eng
Publicado: Springer 2021
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-62704-1
http://cds.cern.ch/record/2752777
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author Bianchini, Bruno
Mari, Luciano
Pucci, Patrizia
Rigoli, Marco
author_facet Bianchini, Bruno
Mari, Luciano
Pucci, Patrizia
Rigoli, Marco
author_sort Bianchini, Bruno
collection CERN
description 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.
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spelling cern-27527772021-04-21T16:43:36Zdoi:10.1007/978-3-030-62704-1http://cds.cern.ch/record/2752777engBianchini, BrunoMari, LucianoPucci, PatriziaRigoli, MarcoGeometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifoldsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:27527772021
spellingShingle Mathematical Physics and Mathematics
Bianchini, Bruno
Mari, Luciano
Pucci, Patrizia
Rigoli, Marco
Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
title Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
title_full Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
title_fullStr Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
title_full_unstemmed Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
title_short Geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
title_sort geometric analysis of quasilinear inequalities on complete manifolds: maximum and compact support principles and detours on manifolds
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-62704-1
http://cds.cern.ch/record/2752777
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AT puccipatrizia geometricanalysisofquasilinearinequalitiesoncompletemanifoldsmaximumandcompactsupportprinciplesanddetoursonmanifolds
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