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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 273959, 11 pages
http://dx.doi.org/10.1155/2013/273959
Research Article

Final State Problem for the Dirac-Klein-Gordon Equations in Two Space Dimensions

Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560 0043, Japan

Received 25 April 2013; Accepted 15 July 2013

Academic Editor: Daniel C. Biles

Copyright © 2013 Masahiro Ikeda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the final state problem for the Dirac-Klein-Gordon equations (DKG) in two space dimensions. We prove that if the nonresonance mass condition is satisfied, then the wave operator for DKG is well defined from a neighborhood at the origin in lower order weighted Sobolev space to some Sobolev space.