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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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User’s guide to viscosity solutions of second order partial differential equations
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by Michael G. Crandall, Hitoshi Ishii and Pierre-Louis Lions PDF
Bull. Amer. Math. Soc. 27 (1992), 1-67 Request permission


The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 27 (1992), 1-67
  • MSC (2000): Primary 35J60; Secondary 35B05, 35D05, 35G20
  • DOI:
  • MathSciNet review: 1118699