Width of Shape Resonances for Non Globally Analytic Potentials
  We consider the semiclassical Schroedinger operator with a "well in an island" potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of a result by Helffer and Sjoestrand in the globally analytic case. We use an almost analytic extension in order to continue the WKB solution coming from the well beyond the caustic set, and, for the justification of the accuracy of this approximation, we develop some refined microlocal arguments in h-dependent small regions. 
S. Fujiie, A. Lahmar-Benbernou, A. Martinez