2009/03/18 by Richard Melrose, Melrose, Richard, András Vasy +3
Mathematics · Physics and Astronomy · Engineering · #Numerical methods in inverse problems #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods
paper · pdf · doi:10.48550/arxiv.0903.3208
We consider the fundamental solution to the wave equation on a manifold with\ncorners of arbitrary codimension. If the initial pole of the solution is\nappropriately situated, we show that the singularities which are diffracted by\nthe corners (i.e., loosely speaking, are not propagated along limits of\ntransversely reflected rays) are smoother than the main singularities of the\nsolution. More generally, we show that subject to a hypothesis of nonfocusing,\ndiffracted wavefronts of any solution to the wave equation are smoother than\nthe incident singularities. These results extend our previous work on edge\nmanifolds to a situation where the fibers of the boundary fibration, obtained\nhere by blowup of the corner in question, are themselves manifolds with\ncorners.\n