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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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