Regularity and energy quantization for the Yang-Mills-Dirac equations on 4-manifolds (Q980894)

The author considers a Yang-Mills-Dirac equation on 4-dimensional Riemannian manifolds and shows that any of its finite energy weak solutions is regular in the sense that it is \(W^{2,2}\cap C^0\)-gauge equivalent to a \(C^\infty\)-solution. Moreover, a compactness-energy quantization effect for the Yang-Mills-Dirac equation is observed and discussed. Interesting arguments involving interpolation spaces and the regularity properties of basic differential operators acting on these interpolation space are used.