We study propagation of microlocal regularities in the Sobolev space of solutions to boundary value problems for the isotropic elastic equation. We assume that the solutions microlocally belong to the Sobolev space of order s on the incident generalized bicharacteristic to the boundary. Then we discuss that whether the solutions have the same microlocal regularities in the Sobolev space on the reflected generalized bicharacteristic or not. Our results depend on the condition that how the incident generalized
bicharacteristic attaches to the boundary. In this paper we only consider the boundary value problems for the isotropic elastic equation, however our method is valid for these
of higher order hyperbolic equations and generalized elastic equations.
Publié le : 2006-08-15
Classification:
elastic equation,
propagation of sigularities,
Sobolev space,
58J47,
35L55
@article{1285766414,
author = {YAMAMOTO, Kazuhiro},
title = {Propagation of microlocal regularities in Sobolev spaces to solutions of boudary value problems for elastic equations},
journal = {Hokkaido Math. J.},
volume = {35},
number = {1},
year = {2006},
pages = { 497-545},
language = {en},
url = {http://dml.mathdoc.fr/item/1285766414}
}
YAMAMOTO, Kazuhiro. Propagation of microlocal regularities in Sobolev spaces to solutions of boudary value problems for elastic equations. Hokkaido Math. J., Tome 35 (2006) no. 1, pp. 497-545. http://gdmltest.u-ga.fr/item/1285766414/