Lp-Theory for Vector Potentials and Sobolev's Inequalities for Vector Fields

7 pagesInternational audienceIn a three dimensional bounded possibly multiply-connected domain, we prove the existence and uniqueness of vector potentials in Lp theory, associated with a divergence-free function and satisfying some boundary conditions. We also present some results concerning scalar potentials and weak vector potentials. Furthermore, variousSobolev-type inequalities are given