Nash equilibria in N-person games with super-quadratic Hamiltonians

摘要

We consider the Hamilton-Jacobi-Bellman system partial differential tu-Delta u=H(u, backward difference u)+ffor u is an element of RN, where the Hamiltonian H(u, backward difference u) satisfies a super-quadratic growth condition with respect to | backward difference u|. Such a non-linear parabolic system corresponds to a stochastic differential game with N players. We obtain the existence of bounded weak solutions and prove regularity results in Sobolev spaces for the Dirichlet problem.