Abstract :
In this paper we introduce and discuss, in the Clifford algebra framework,
certain Hardy-like spaces which are well suited for the study of the Helmholtz
equation Duqk2us0 in Lipschitz domains of Rnq1. In particular, in the second
part of the paper, these results are used in connection with the classical boundary
value problems for the Helmholtz equation in Lipschitz domains in arbitrary space
dimensions. In this setting, existence, uniqueness, and optimal estimates are
obtained by inverting the corresponding layer potential operators on L p for sharp
ranges of p’s. Also, a detailed discussion of the Helmholtz eigenvalues of Lipschitz
domains is presented.
