Besov regularity for operator equations on patchwise smooth manifolds

We study regularity properties of solutions to operator equations on patchwise smooth manifolds  ∂ Ω , e.g., boundaries of polyhedral domains Ω ⊂ R 3 . Using suitable biorthogonal wavelet bases Ψ , we introduce a new class of Besov-type spaces B Ψ , q α ( L p ( ∂ Ω ) ) of functions u : ∂ Ω → C . Spe...

Full description

Saved in:
Bibliographic Details
Published in:Foundations of computational mathematics 2015-10, Vol.15 (6), p.1533-1569
Main Authors: Dahlke, Stephan, Weimar, Markus
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Computer Science
Economics
Linear and Multilinear Algebras
Manifolds (Mathematics)
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Transformations (Mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study regularity properties of solutions to operator equations on patchwise smooth manifolds  ∂ Ω , e.g., boundaries of polyhedral domains Ω ⊂ R 3 . Using suitable biorthogonal wavelet bases Ψ , we introduce a new class of Besov-type spaces B Ψ , q α ( L p ( ∂ 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 B Ψ , τ α ( L τ ( ∂ 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 .
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-015-9273-9