Weak Vector and Scalar Potentials: Applications to Poincaré's Theorem and Korn's Inequality in Sobolev Spaces With Negative Exponents

In this paper, we present several results concerning vector potentials and scalar potentials with data in Sobolev spaces with negative exponents, in a not necessarily simply-connected, three-dimensional domain. We then apply these results to Poincaré's theorem and to Korn's inequality.