Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians

Abstract

We establish general representation formulas for solu- tions of Hamilton-Jacobi equations with convex Hamiltonians. In or- der to treat representation formulas on general domains, we introduce a notion of ideal boundary similar to the Martin boundary (21 )i n po- tential theory. We apply such representation formulas to investigate maximal solutions, in certain classes of functions, of Hamilton-Jacobi equations. Part of the results in this paper has been announced in (22).