• Marta Lewicka
Part of the Universitext book series (UTX)


This chapter contains the introductory discussion of: the linear motivation for the topic, the nonlinear motivation, the whys and wherefores, the description of the book’s content, prerequisites, notation and acknowledgements.



In preparing these Course Notes, the author has greatly benefited from discussions with Y. Peres, whose seminal work from a decade ago uncovered the deep connections between Nonlinear Potential Theory and Stochastic Processes. The author wishes to thank Y. Peres for advising her studies of Game Theory and Probability, in the oftentimes limiting context of the author’s analysis-trained and oriented point of view.

The gratitude extends to J. Manfredi for introducing the author to the topic of this book, for discussions on p-Laplacian and viscosity solutions and for coauthoring joint papers. The author is further grateful to P. Lindqvist for discussions and the continuous kind encouragement.

An acknowledgement is due to Microsoft Research, whose financial support allowed for the author’s visits to MSR Redmond in the early stages of this work. As a final word, the author would like to bring the readers’ attention to the recent book by Blanc and Rossi (2019), which is concerned with the same topic as these Course Notes, albeit written with different scope and style.


  1. P. Blanc and J.D. Rossi. Game theory and partial differential equations. volume 31 of Nonlinear Analysis and Applications. De Gruyter Series, 2019.Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Marta Lewicka
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA

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