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Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
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Edited by:
Alexander Grigor'yan
Language:
English
Published/Copyright:
2021
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 / Editor information
Alexander Grigor’yan, University of Bielefeld, Germany and Yuhua Sun, Nankai University, China.
Topics
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Frontmatter
I -
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Contents
V -
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Preface
VII - Part I: Fractals and graphs
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Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes
1 -
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The pointwise existence and properties of heat kernel
27 -
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Resistance estimates and critical exponents of Dirichlet forms on fractals
71 -
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A survey on unbounded Laplacians and intrinsic metrics on graphs
103 -
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Energy measures for diffusions on fractals: a survey
119 -
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Hyperbolic graphs induced by iterations and applications in fractals
143 -
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Geometric implications of fast volume growth and capacity estimates
183 -
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Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set
201 -
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Metrics and uniform Harnack inequality on the Strichartz hexacarpet
275 - Part II: Euclidean spaces and manifolds
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Analysis on manifolds and volume growth
299 -
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Geometric analysis on manifolds with ends
325 -
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A matrix Harnack estimate for a Kolmogorov type equation
345 -
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Entropy power concavity inequality on Riemannian manifolds and Ricci flow
359 -
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Fractional differential operators and divergence equations
385 -
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Interior gradient estimates for mean curvature type equations and related flows
421 -
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An alternate induction argument in Simons’ proof of holonomy theorem
443 -
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Higher integrability for nonlinear nonlocal equations with irregular kernel
459 -
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On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds
493 -
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Index
515
Publishing information
Pages and Images/Illustrations in book
eBook published on:
January 18, 2021
eBook ISBN:
9783110700763
Hardcover published on:
January 18, 2021
Hardcover ISBN:
9783110700633
Pages and Images/Illustrations in book
Front matter:
8
Main content:
518
Illustrations:
30
Keywords for this book
Partielle Differenzialgleichung
Audience(s) for this book
Researches in Mathematics, Advanced Graduate Students interested in the field.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
