A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians
Analysis of PDEs
2010-03-19 v2
Abstract
We construct a frame of complex Gaussians for the space of functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the coefficients of the wave equation have more regularity, propagated frame functions become Gaussian beams.
Cite
@article{arxiv.1003.2747,
title = {A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians},
author = {Alden Waters},
journal= {arXiv preprint arXiv:1003.2747},
year = {2010}
}