The Helmholtz decomposition in Sobolev and Besov spaces

Abstract

This paper is concerned with the Helmholtz decomposition of vector fields on bounded domains and exterior domains, and provides the decompositions in Sobolev spaces and Besov spaces of order in certain interval. In particular, the decompositions in homogeneous Besov spaces $\dot{B}_{1,q}^{s}$ and $\dot{B}_{\infty,q}^{s}$ are given.