High Quality Content by WIKIPEDIA articles! In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael Crandall as a generalization of the classical concept of what is meant by a `solution` to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE`s, including for example first order equations arising in optimal control (the Hamilton-Jacobi equation), differential games (the Isaacs equation) or front evolution problems, as well as second-order equations such as the ones arising in stochastic optimal control or stochastic differential games.