L 3/2-estimates of vector fields with L 1 curl in a bounded domain

This paper establishes the estimates of L ^3/2 norm of the vector fields in a bounded domain with vanishing tangential component on the boundary, in terms of the L ¹ norm of the curl, the negative exponent Sobolev norm of the divergence, and on some quantities depending on the topology of the domain. As the similar proof we also obtain the estimates of L ^p norm of the vector fields in terms of the negative exponent Sobolev norms of the curl and divergence.