Suppose we have the wave type equation $$\partial^2_tu - L u = 0$$ on a compact manifold with boundary, where $L$ is a second order strongly elliptic operator with coercive boundary conditions (not necessarily Dirichlet or Neumann) making it self-adjoint. I wanted some references for $L^p$ regularity results for such equations, if such results exist at all. I don't think the standard Calderon-Zygmund theory or the standard pseudodifferential approach hold because of the boundary conditions. Thank you in advance.