Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces. (Record no. 16243)
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| fixed length control field | 04951nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC6118470 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114122.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2019 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470455132 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470439132 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC6118470 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL6118470 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1140400914 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA611.28 |
| Item number | .A437 2019 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514.32000000000005 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Ambrosio, Luigi. |
| 245 10 - TITLE STATEMENT | |
| Title | Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2019. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (134 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.262 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Contraction and Convexity via Hamiltonian Estimates: an Heuristic Argument -- Part I . Nonlinear Diffusion Equations and Their Linearization in Dirichlet Spaces -- Chapter 3. Dirichlet Forms, Homogeneous Spaces and Nonlinear Diffusion -- 3.1. Dirichlet forms -- 3.2. Completion of quotient spaces w.r.t. a seminorm -- 3.3. Nonlinear diffusion -- Chapter 4. Backward and Forward Linearizations of Nonlinear Diffusion -- Part II . Continuity Equation and Curvature Conditions in Metric Measure Spaces -- Chapter 5. Preliminaries -- 5.1. Absolutely continuous curves, Lipschitz functions and slopes -- 5.2. The Hopf-Lax evolution formula -- 5.3. Measures, couplings, Wasserstein distance -- 5.4. _{ }-absolutely continuous curves and dynamic plans -- 5.5. Metric measure spaces and the Cheeger energy -- 5.6. Entropy estimates of the quadratic moment and of the Fisher information along nonlinear diffusion equations -- 5.7. Weighted Γ-calculus -- Chapter 6. Absolutely Continuous Curves in Wasserstein Spaces and Continuity Inequalities in a Metric Setting -- Chapter 7. Weighted Energy Functionals along Absolutely Continuous Curves -- Chapter 8. Dynamic Kantorovich Potentials, Continuity Equation and Dual Weighted Cheeger Energies -- Chapter 9. The \RCDS Condition and Its Characterizations through Weighted Convexity and Evolution Variational Inequalities -- 9.1. Green functions on intervals -- 9.2. Entropies and their regularizations -- 9.3. The \CDS condition and its characterization via weighted action convexity -- 9.4. \RCD ∞ spaces and a criterium for \CDS via -- Part III . Bakry-Émery Condition and Nonlinear Diffusion -- Chapter 10. The Bakry-Émery Condition -- 10.1. The Bakry-Émery condition for local Dirichlet forms and interpolation estimates. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 10.2. Local and "nonlinear" characterization of the metric \BE condition in locally compact spaces -- Chapter 11. Nonlinear Diffusion Equations and Action Estimates -- Chapter 12. The Equivalence Between \BE and \RCDS -- 12.1. Regular curves and regularized entropies -- 12.2. \BE yields for regular entropy functionals in \MC -- 12.3. \RCDS implies \BE -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,\mathsf d,\mathfrak m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong \mathrm {CD}^{*}(K,N) condition of Bacher-Sturm. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Metric spaces. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Mondino, Andrea. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Savaré, Giuseppe. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Ambrosio, Luigi |
| Title | Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2019 |
| International Standard Book Number | 9781470439132 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6118470">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6118470</a> |
| Public note | Click to View |
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