The existence and uniqueness of solutions of Yang-Mills equations with bag boundary conditions

The Cauchy problem for the Yang-Mills equations in the Coulomb gauge is studied on a compact, connected and simply connected Riemannian manifold with boundary. An existence and uniqueness theorem for the evolution equations is proven for fields with Cauchy data in an appropriate Sobolev space. The proof is based the Hodge decomposition of the Yang-Mills fields and the theory of non-linear semigroups.Work partially supported by NSERC Research Grant A 8091Work supported by DFG Grant Schw 485/2-1