Besov regularity for operator equations on patchwise smooth manifolds

We study regularity properties of solutions to operator equations on patchwise smooth manifolds partial derivative Omega, e.g., boundaries of polyhedral domains Omega subset of R-3. Using suitable biorthogonal wavelet bases Psi, we introduce a new class of Besov-type spaces B-Psi,q(alpha) (L-p(partial derivative Omega)) of functions u : partial derivative Omega -> C. Special attention is paid on the rate of convergence for best n-term wavelet approximation to functions in these scales since this determines the performance of adaptive numerical schemes. We show embeddings of (weighted) Sobolev spaces on partial derivative Omega into B-Psi,tau(alpha) (L-tau(partial derivative Omega)), 1/tau = alpha/2 + 1/2, which lead us to regularity assertions for the equations under consideration. Finally, we apply our results to a boundary integral equation of the second kind which arises from the double-layer ansatz for Dirichlet problems for Laplace's equation in Omega.