| We introduce a general approach to construct global discontinuous solutions of Hamilton-Jacobi equations. Our approach allows the Cauchy data only in Linfinity and applies to the equations with non-convex Hamiltonians. The profit functions are introduced to formulate our new notion of discontinuous solutions. The existence of global discontinuous solutions in Linfinity is established. Our solutions in Linfinity coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the uniqueness and stability of discontinuous solutions. |
