SpringerBriefs in Mathematics

Regularity Theory for Mean-Field Game Systems

Authors: Gomes, Diogo A., Pimentel, Edgard A., Voskanyan, Vardan

  • ​Details key elements of the regularity theory for mean-field games
  • Presents a series of techniques for well-posedness 
  • Explores stationary and time-dependent MFGs through a series of a-priori estimates​
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eBook $39.99
price for Brazil (gross)
  • ISBN 978-3-319-38934-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for Brazil
  • ISBN 978-3-319-38932-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (11 chapters)

  • Introduction

    Gomes, Diogo A. (et al.)

    Pages 1-8

  • Explicit Solutions, Special Transformations, and Further Examples

    Gomes, Diogo A. (et al.)

    Pages 9-14

  • Estimates for the Hamilton–Jacobi Equation

    Gomes, Diogo A. (et al.)

    Pages 15-37

  • Estimates for the Transport and Fokker–Planck Equations

    Gomes, Diogo A. (et al.)

    Pages 39-61

  • The Nonlinear Adjoint Method

    Gomes, Diogo A. (et al.)

    Pages 63-76

Buy this book

eBook $39.99
price for Brazil (gross)
  • ISBN 978-3-319-38934-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for Brazil
  • ISBN 978-3-319-38932-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Regularity Theory for Mean-Field Game Systems
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-38934-9
DOI
10.1007/978-3-319-38934-9
Softcover ISBN
978-3-319-38932-5
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIV, 156
Number of Illustrations and Tables
4 illustrations in colour
Topics