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.
"Final State Problem for the Dirac-Klein-Gordon Equations in Two Space Dimensions." Abstr. Appl. Anal. 2013 (SI29) 1 - 11, 2013. https://doi.org/10.1155/2013/273959