The Mixed Dirichlet]Neumann]Cauchy Problem for Second Order Hyperbolic Operators

A hyperbolic mixed initial boundary-value problem is investigated in which the Neumann condition and the Dirichlet condition are given on complementary parts of the boundary. An existence and uniqueness result in Sobolev spaces with additional differentiation in the tangential directions to the interface is proved by obtaining energy estimates and applying a duality argument. The goal is the eventual analysis by the Wiener]Hopf method of the asymptotic behavior of the solution near the interface