Maximal generalized solutions of Hamilton–Jacobi equations

We study the Dirichlet problem for Hamilton–Jacobi equations of the form (Formula presented.), without continuity assumptions on the hamiltonian H with respect to the variable x. We find a class of Caratheodory functions H for which the problem admits a (maximal) generalized solution which, in the continuous case, coincides with the classical viscosity solution. © 2016, Università degli Studi di Ferrara.