Variational Problem Involving Operator Curl in a Multiconnected Domain

We shall study the problem of minimizing a functional involving the curl of vector fields in a three-dimensional, bounded multiconnected domain with prescribed tangential component on the boundary. The paper is an extension of L2 minimization problem of the curl of vector fields. We shall prove the existence and the estimate of minimizers of more general functional which contains Lp norm of the curl of vector fields