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Geometric analysis of quasilinear in...

Bianchini, Bruno.

Geometric analysis of quasilinear inequalities on complete manifoldsmaximum and compact support principles and detours on manifolds /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric analysis of quasilinear inequalities on complete manifoldsby Bruno Bianchini ... [et al.].
Reminder of title:	maximum and compact support principles and detours on manifolds /
other author:	Bianchini, Bruno.
Published:	Cham :Springer International Publishing :2021.
Description:	x, 286 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Riemannian manifolds.
Online resource:	https://doi.org/10.1007/978-3-030-62704-1
ISBN:	9783030627041$q(electronic bk.)

Geometric analysis of quasilinear inequalities on complete manifoldsmaximum and compact support principles and detours on manifolds /
Geometric analysis of quasilinear inequalities on complete manifoldsmaximum and compact support principles and detours on manifolds /[electronic resource] :by Bruno Bianchini ... [et al.]. - Cham :Springer International Publishing :2021. - x, 286 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

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.

ISBN: 9783030627041$q(electronic bk.)

Standard No.: 10.1007/978-3-030-62704-1doiSubjects--Topical Terms:

190949
Riemannian manifolds.

LC Class. No.: QA671

Dewey Class. No.: 516.373

Geometric analysis of quasilinear inequalities on complete manifoldsmaximum and compact support principles and detours on manifolds /
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520 $a 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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