Variational problem involving operator curl associated with p-curl system

Abstract

We shall study the problem of minimizing a functional involving curl of vector fields in a three-dimensional,bounded multiconnected domain with the prescribed tangent component of a given vector field on the boundary. It willbe seen that the minimizers are weak solutions of the p-curl type system. We shall prove the existence and the estimateof minimizers of a more general functional that contains the $L^p$ norm of the curl of vector fields. We shall also give thecontinuity with respect to the given data.