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The Resource Regularity theory for mean field games systems, Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan

Regularity theory for mean field games systems, Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan

Label
Regularity theory for mean field games systems
Title
Regularity theory for mean field games systems
Statement of responsibility
Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Creator
Contributor
Author
Subject
Language
eng
Summary
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields
Member of
Cataloging source
YDX
http://library.link/vocab/creatorName
Gomes, Diogo A
Dewey number
530.14/4
Index
index present
LC call number
QC174.85.M43
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Pimentel, Edgard A.
  • Voskanyan, Vardan
Series statement
SpringerBriefs in mathematics
http://library.link/vocab/subjectName
  • Mean field theory
  • Game theory
Label
Regularity theory for mean field games systems, Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Book Outline; Thanks; Bibliographical Notes; Acknowledgments; Contents; 1 Introduction; 1.1 Derivation of MFG Models; 1.1.1 Optimal Control and Hamilton-Jacobi Equations; 1.1.2 Transport Equation; 1.1.3 Mean-Field Models; 1.1.4 Extensions and Additional Problems; 1.1.5 Uniqueness; 2 Explicit Solutions, Special Transformations, and Further Examples; 2.1 Explicit Solutions; 2.2 The Hopf-Cole Transform; 2.3 Gaussian-Quadratic Solutions; 2.4 Interface Formation; 2.5 Bibliographical Notes; 3 Estimates for the Hamilton-Jacobi Equation; 3.1 Comparison Principle; 3.2 Control Theory Bounds
  • 3.2.1 Optimal Trajectories3.2.2 Dynamic Programming Principle; 3.2.3 Subdifferentials and Superdifferentials of the Value Function; 3.2.4 Regularity of the Value Function; 3.3 Integral Bernstein Estimate; 3.4 Integral Estimates for HJ Equations; 3.5 Gagliardo-Nirenberg Estimates; 3.6 Bibliographical Notes; 4 Estimates for the Transport and Fokker-Planck Equations; 4.1 Mass Conservation and Positivity of Solutions; 4.2 Regularizing Effects of the Fokker-Planck Equation; 4.3 Fokker-Planck Equation with Singular Initial Conditions; 4.4 Iterative Estimates for the Fokker-Planck Equation
  • 4.4.1 Regularity by Estimates on the Divergence of the Drift4.4.2 Polynomial Estimates for the Fokker-Planck Equation, p<&#x221E;; 4.4.3 Polynomial Estimates for the Fokker-Planck Equation, p=&#x221E;; 4.5 Relative Entropy; 4.6 Weak Solutions; 4.7 Bibliographical Notes; 5 The Nonlinear Adjoint Method; 5.1 Representation of Solutions and Lipschitz Bounds; 5.2 Conserved Quantities; 5.3 The Vanishing Viscosity Convergence Rate; 5.4 Semiconcavity Estimates; 5.5 Lipschitz Regularity for the Heat Equation; 5.6 Irregular Potentials; 5.7 The Hopf-Cole Transform; 5.8 Bibliographical Notes; 6 Estimates for MFGs
  • 6.1 Maximum Principle Bounds6.2 First-Order Estimates; 6.3 Additional Estimates for Solutions of the Fokker-Plank Equation; 6.4 Second-Order Estimates; 6.4.1 Stationary Problems; 6.4.2 Time-Dependent Problems; 6.5 Some Consequences of Second-Order Estimates; 6.6 The Evans Method for the Evans-Aronsson Problem; 6.7 An Energy Conservation Principle; 6.8 Porreta's Cross Estimates; 6.9 Bibliographical Notes; 7 A Priori Bounds for Stationary Models; 7.1 The Bernstein Method; 7.2 A MFG with Congestion; 7.3 Logarithmic Nonlinearity; 7.4 Bibliographical Notes
  • 8 A Priori Bounds for Time-Dependent Models8.1 Subquadratic Hamiltonians; 8.2 Quadratic Hamiltonians; 8.3 Bibliographical Notes; 9 A Priori Bounds for Models with Singularities; 9.1 Logarithmic Nonlinearities; 9.2 Congestion Models: Local Existence; 9.2.1 Estimates for Arbitrary Terminal Time; 9.2.2 Short-Time Estimates; 9.3 Bibliographical Notes; 10 Non-local Mean-Field Games: Existence; 10.1 First-Order, Non-local Mean-Field Games; 10.2 Second-Order, Non-local Mean-Field Games; 10.3 Bibliographical Notes; 11 Local Mean-Field Games: Existence; 11.1 Bootstrapping Regularity
Control code
SPR958864856
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319389325
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
Label
Regularity theory for mean field games systems, Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Book Outline; Thanks; Bibliographical Notes; Acknowledgments; Contents; 1 Introduction; 1.1 Derivation of MFG Models; 1.1.1 Optimal Control and Hamilton-Jacobi Equations; 1.1.2 Transport Equation; 1.1.3 Mean-Field Models; 1.1.4 Extensions and Additional Problems; 1.1.5 Uniqueness; 2 Explicit Solutions, Special Transformations, and Further Examples; 2.1 Explicit Solutions; 2.2 The Hopf-Cole Transform; 2.3 Gaussian-Quadratic Solutions; 2.4 Interface Formation; 2.5 Bibliographical Notes; 3 Estimates for the Hamilton-Jacobi Equation; 3.1 Comparison Principle; 3.2 Control Theory Bounds
  • 3.2.1 Optimal Trajectories3.2.2 Dynamic Programming Principle; 3.2.3 Subdifferentials and Superdifferentials of the Value Function; 3.2.4 Regularity of the Value Function; 3.3 Integral Bernstein Estimate; 3.4 Integral Estimates for HJ Equations; 3.5 Gagliardo-Nirenberg Estimates; 3.6 Bibliographical Notes; 4 Estimates for the Transport and Fokker-Planck Equations; 4.1 Mass Conservation and Positivity of Solutions; 4.2 Regularizing Effects of the Fokker-Planck Equation; 4.3 Fokker-Planck Equation with Singular Initial Conditions; 4.4 Iterative Estimates for the Fokker-Planck Equation
  • 4.4.1 Regularity by Estimates on the Divergence of the Drift4.4.2 Polynomial Estimates for the Fokker-Planck Equation, p<&#x221E;; 4.4.3 Polynomial Estimates for the Fokker-Planck Equation, p=&#x221E;; 4.5 Relative Entropy; 4.6 Weak Solutions; 4.7 Bibliographical Notes; 5 The Nonlinear Adjoint Method; 5.1 Representation of Solutions and Lipschitz Bounds; 5.2 Conserved Quantities; 5.3 The Vanishing Viscosity Convergence Rate; 5.4 Semiconcavity Estimates; 5.5 Lipschitz Regularity for the Heat Equation; 5.6 Irregular Potentials; 5.7 The Hopf-Cole Transform; 5.8 Bibliographical Notes; 6 Estimates for MFGs
  • 6.1 Maximum Principle Bounds6.2 First-Order Estimates; 6.3 Additional Estimates for Solutions of the Fokker-Plank Equation; 6.4 Second-Order Estimates; 6.4.1 Stationary Problems; 6.4.2 Time-Dependent Problems; 6.5 Some Consequences of Second-Order Estimates; 6.6 The Evans Method for the Evans-Aronsson Problem; 6.7 An Energy Conservation Principle; 6.8 Porreta's Cross Estimates; 6.9 Bibliographical Notes; 7 A Priori Bounds for Stationary Models; 7.1 The Bernstein Method; 7.2 A MFG with Congestion; 7.3 Logarithmic Nonlinearity; 7.4 Bibliographical Notes
  • 8 A Priori Bounds for Time-Dependent Models8.1 Subquadratic Hamiltonians; 8.2 Quadratic Hamiltonians; 8.3 Bibliographical Notes; 9 A Priori Bounds for Models with Singularities; 9.1 Logarithmic Nonlinearities; 9.2 Congestion Models: Local Existence; 9.2.1 Estimates for Arbitrary Terminal Time; 9.2.2 Short-Time Estimates; 9.3 Bibliographical Notes; 10 Non-local Mean-Field Games: Existence; 10.1 First-Order, Non-local Mean-Field Games; 10.2 Second-Order, Non-local Mean-Field Games; 10.3 Bibliographical Notes; 11 Local Mean-Field Games: Existence; 11.1 Bootstrapping Regularity
Control code
SPR958864856
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319389325
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote

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