Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs

Published by De Gruyter 2021

Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs

Edited by: Alexander Grigor'yan and Yuhua Sun

Volume 3 in the series Advances in Analysis and Geometry

https://doi.org/10.1515/9783110700763

Overview
Contents

About this book

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.

Current research and surveys on the topic of PDEs.
Written by leading researchers in the field.

Author information

Alexander Grigor’yan, University of Bielefeld, Germany and Yuhua Sun, Nankai University, China.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Preface Publicly Available Download PDF	VII
Part I: Fractals and graphs
Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes Zhen-Qing Chen, Takashi Kumagai and Jian Wang Requires Authentication Unlicensed Licensed Download PDF	1
The pointwise existence and properties of heat kernel Alexander Grigor’yan, Eryan Hu and Jiaxin Hu Requires Authentication Unlicensed Licensed Download PDF	27
Resistance estimates and critical exponents of Dirichlet forms on fractals Qingsong Gu and Ka-Sing Lau Requires Authentication Unlicensed Licensed Download PDF	71
A survey on unbounded Laplacians and intrinsic metrics on graphs Bobo Hua and Xueping Huang Requires Authentication Unlicensed Licensed Download PDF	103
Energy measures for diffusions on fractals: a survey Naotaka Kajino Requires Authentication Unlicensed Licensed Download PDF	119
Hyperbolic graphs induced by iterations and applications in fractals Shi-Lei Kong, Ka-Sing Lau, Jun Jason Luo and Xiang-Yang Wang Requires Authentication Unlicensed Licensed Download PDF	143
Geometric implications of fast volume growth and capacity estimates Tim Jaschek and Mathav Murugan Requires Authentication Unlicensed Licensed Download PDF	183
Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set Ryosuke Shimizu Requires Authentication Unlicensed Licensed Download PDF	201
Metrics and uniform Harnack inequality on the Strichartz hexacarpet Meng Yang Requires Authentication Unlicensed Licensed Download PDF	275
Part II: Euclidean spaces and manifolds
Analysis on manifolds and volume growth Alexander Grigor’yan Requires Authentication Unlicensed Licensed Download PDF	299
Geometric analysis on manifolds with ends Alexander Grigor’yan, Satoshi Ishiwata and Laurent Saloff-Coste Requires Authentication Unlicensed Licensed Download PDF	325
A matrix Harnack estimate for a Kolmogorov type equation Feida Jiang and Xinyi Shen Requires Authentication Unlicensed Licensed Download PDF	345
Entropy power concavity inequality on Riemannian manifolds and Ricci flow Songzi Li and Xiang-Dong Li Requires Authentication Unlicensed Licensed Download PDF	359
Fractional differential operators and divergence equations Liguang Liu and Jie Xiao Requires Authentication Unlicensed Licensed Download PDF	385
Interior gradient estimates for mean curvature type equations and related flows Li Ma Requires Authentication Unlicensed Licensed Download PDF	421
An alternate induction argument in Simons’ proof of holonomy theorem Lei Ni Requires Authentication Unlicensed Licensed Download PDF	443
Higher integrability for nonlinear nonlocal equations with irregular kernel Simon Nowak Requires Authentication Unlicensed Licensed Download PDF	459
On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds Yuhua Sun and Fanheng Xu Requires Authentication Unlicensed Licensed Download PDF	493
Index Requires Authentication Unlicensed Licensed Download PDF	515

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researches in Mathematics, Advanced Graduate Students interested in the field.
Pages
- Front matter: 8
- Main content: 518
Illustrations
- Illustrations: 30
Keywords: Partielle Differenzialgleichung

eBook

Published: January 18, 2021
ISBN: 9783110700763

Hardcover

Published: January 18, 2021
ISBN: 9783110700633