Asymptotic expansions of double oscillatory integrals with a curve of stationary points (Q2745748)

Let \(D\) be a bounded plane domain with smooth boundary and let \(f\) and \(g\) be two real functions, \(C^\infty\) up to the boundary in \(D\). Assuming that the critical set of \(f\) is a simple curve of class \(C^\infty\), the authors study the asymptotic expansion of the oscillatory integral NEWLINE\[NEWLINEI(\lambda)= \iint_D g(x,y) e^{i\lambda f(x,y)}dx dyNEWLINE\]NEWLINE for \(\lambda\to +\infty\). They deal with more general situations than in previous works on the subject: for instance, the case of curves \(\gamma\) intersecting \(\partial D\) tangentially is studied.