We study regularity properties of solutions to operator equations on
patchwise smooth manifolds ∂Ω such as, e.g., boundaries of
polyhedral domains Ω⊂R3. Using suitable biorthogonal
wavelet bases Ψ, we introduce a new class of Besov-type spaces
BΨ,qα(Lp(∂Ω)) of functions
u:∂Ω→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 ∂Ω
into BΨ,τα(Lτ(∂Ω)), 1/τ=α/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 Ω.Comment: 42 pages, 3 figures, updated after peer review. Preprint: Bericht
Mathematik Nr. 2013-03 des Fachbereichs Mathematik und Informatik,
Universit\"at Marburg. To appear in J. Found. Comput. Mat