A nonvariational form of the acoustic single layer potential

We consider a bounded open subset ohm of R-n of class C-1,C-alpha for some alpha is an element of]0, 1[ and the space V- -1,V-alpha(partial derivative ohm) of (distributional) normal derivatives on the boundary of alpha-H & ouml;lder continuous functions in ohm that have Laplace operator in the Schauder space with negative exponent C--1,C-alpha(ohm). Then, we prove those properties of the acoustic single layer potential that are necessary to analyze the Neumann problem for the Helmholtz equation in ohm with boundary data in V (-1,alpha)(partial derivative ohm) and solutions in the space of alpha-H & ouml;lder continuous functions in ohm that have Laplace operator in C--1,C-alpha (ohm), i.e., in a space of functions that may have infinite Dirichlet integral. Namely, this a Neumann problem that does not belong to the classical variational setting.