  In this work we consider the Neumann problem for the Laplace operator and we
prove an existence result in the H\"older spaces and obtain Schauder estimates.
According to our knowledge this result is not explicitly proved in the several
works devoted to the Schauder theory, where similar theorems are proved in
detail for the Dirichlet and oblique derivative problems. Our contribution is
to make explicit the existence and the estimate for the Neumann problem.
