An integro-extremization approach for non coercive and evolution Hamilton-Jacobi equations

We devote the integro-extremization method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations mathematical equation represented with a particular interest for non coercive hamiltonians F, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations mathematical equation represented. We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian F, on the domain Ω and on the boundary datum, without any growth assumptions on F. © Heldermann Verlag.