Method of stationary phase for double integrals

Question

I am looking for a reference for the leading term in the asymptotics of a double integral over a finite rectangle R of $K(x,y)\exp(i \,t\, h(x,y))$ as $t \to \infty$ in the following situation: the real valued function $h(x,y)$ has a non-degenerate critical point $P$ which is an interior point of R and $K(x,y)$ is discontinuous at the same point, $P$.