The Lax solution to a Hamilton–Jacobi equation and its generalizations: Part 2 Original Research Article

It is proved that the function defined by the infimum-based Lax formula (for viscosity solutions) provides a solution almost everywhere in x for each fixed t>0 to the Hamilton–Jacobi, Cauchy problem View the MathML source where the Cauchy data function v is lower semicontinuous on real n-space. In addition, a generalization of the Lax formula is developed for the more inclusive Hamilton–Jacobi equation View the MathML source where J is a diagonal, positive-definite matrix.