Nonlinear A-Dirac Equations

This paper is a study of solutions to nonlinear Dirac equations, in domains in Euclidean space, which are generalizations of the Clifford Laplacian as well as elliptic equations in divergence form. A Caccioppoli estimate is used to prove a global integrability theorem for the image of a solution under the Euclidean Dirac operator. Oscillation spaces for Clifford valued functions are used which generalize the usual spaces of bounded mean oscillation, local Lipschitz continuity or local order of growth of real-valued functions.