Viscosity solution

A viscosity solution is a type of weak solution to certain types of nonlinear partial differential equations (PDEs), particularly those of the Hamilton-Jacobi type. The concept is particularly useful in cases where classical solutions may not exist, such as when solutions may be discontinuous or exhibit other singular behaviors. ### Definition A viscosity solution satisfies the PDE in a "viscosity" sense, which means it adheres to a specific geometric interpretation involving test functions.