2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171336For a $n$-dimensional spin manifold $M$ with a fixed spin structure and a spinor bundle $ΣM$, we prove an $ε$-regularity theorem for weak solutions to the nonlinear Dirac equation of cubic nonlinearity. This, in particular, answers a regularity question raised by Chen-Jost-Wang when $n=2$.6pagesAnalysis of PDEsDifferential Geometry35J20text