Viscosity solutions for measurable Hamilton–Jacobi equations

Antonio Siconolfi – University Roma La Sapienza

We consider a class of Hamilton–Jacobi equations whose Hamiltonians are only measurable with respect to the state variable, in IR^{N} or on a compact manifold M.

We adapt the definition of viscosity solution to the measurable setting and show the existence of such solutions on open proper subsets. Global solutions are also obtained if the equation is given in IR^{N} or under additional assumptions on the compact manifold M.

We present representation formulae, comparison principles and homogenisation results.