LAUSR

Abstract In this paper we study a nonlinear magneto-static model on a general domain in R 3 which is multiply-connected and has holes, and under a nonlinear relation between the magnetic induction B and the magnetic field H. The equation of the model contains a Neumann field h 1 ∈ H 1 ( Ω ) and a Dirichlet field h 2 ∈ H 2 ( Ω ) , which represent the effects of domain topology. In the case of a general electric current, the equation contains also an unknown gradient ∇ p ( x ) , which represents the electric field. Existence results of solutions of the boundary value problems of this model and of a more general nonlinear Maxwell-Stokes system with topological parameters h 1 and h 2 are proved, which exhibit the effects of domain topology on the electromagnetic fields and on the nonlinear systems involving curl .