user's guide to viscosity solutions of second order partial differential   equations
  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. 
Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions