Analytic Wave Front Set for Solutions to Schrodinger Equations II - Long Range Perturbations

作者：Martinez Andre^*; Nakamura Shu; Sordoni Vania

来源：Communications in Partial Differential Equations, 2010, 35(12): 2279-2309.

DOI：10.1080/03605302.2010.523918

• Analytic singularities
• Infinite propagation speed
• Subquadratic potentials

This paper is a continuation of [9], where short range perturbations of the flat Euclidian metric where considered. Here, we generalize the results of [9] to long-range perturbations (in particular, we can allow potentials growing like < x > 2-epsilon at infinity). More precisely, we construct a modified quantum free evolution G0(-s, hDz) acting on Sjostrand's spaces, and we characterize the analytic wave front set of the solution e-itHu0 of the Schrodinger equation, in terms of the semiclassical exponential decay of G0(-th-1, hDz)Tu0, where T stands for the Bargmann-transform. The result is valid for t0 near the forward non trapping points, and for t0 near the backward non trapping points. It is an extension of [12] to the analytic framework.

• 出版日期2010