Hokkaido Mathematical Journal

YAMAMOTO Kazuhiro,

Propagation of microlocal regularities in Sobolev spaces to solutions of boudary value problems for elastic equations.

Hokkaido Mathematical Journal, 35 (2006) pp.497-545

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Abstract

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.

MSC(Primary)58J47
MSC(Secondary)35L55
Uncontrolled Keywordselastic equation, propagation of sigularities, Sobolev space