LP(x)(ʊ)-estimates of vector fields and some applications to magnetostatics problems

In the present paper, we investigate Hölder-type norm inequalities in terms of div and curl of the vector-valued functions in variable exponent Lebesgue spaces L p ( x ) ( Ω ) , where Ω ⊂ R 3 . Moreover, by using the obtained results we give some applications for magnetostatics problems.