Asymptotic expansions of double oscillatory integrals with a curve of stationary points

In this Note, ive shall consider asymptotic expansions of integrals I(lambd a) = integral (D) g . e(i lambdaf) dx, ii,here D is a bidimensional bounded domain, f and g are two C-infinity functions, and the set gamma of station ary points of the phase f is a C-infinity simple curve in (D) over bar. In the contrary to the previous results, the expansions realized here are more explicit and obtained under weaker conditions and in more general situatio ns than in the case where the curve gamma cuts tangentially the boundary of D. Moreover the influence of the geometry of gamma is taken into account. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.