Remark on the Helmholtz decomposition in domains with noncompact boundary

Abstract

Let $\Omega$ be a domain with noncompact boundary. It is known that the Helmholtz decomposition is not always valid in $L^p(\Omega )$ except for the energy space $L^2(\Omega )$. In this paper we consider a typical unbounded domain whose boundary is given as a Lipschitz graph, and show that the Helmholtz decomposition holds in certain anisotropic spaces which include some infinite energy vector fields.

References in corpus (1)

• Analyticity of layer potentials and $L^2$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty }$ coefficients

Cited by in corpus (1)

• On domain of Poisson operators and factorization for divergence form elliptic operators