{"paper":{"title":"Besov regularity for operator equations on patchwise smooth manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NA","authors_text":"Markus Weimar, Stephan Dahlke","submitted_at":"2013-12-10T09:58:53Z","abstract_excerpt":"We study regularity properties of solutions to operator equations on patchwise smooth manifolds $\\partial\\Omega$ such as, e.g., boundaries of polyhedral domains $\\Omega \\subset \\mathbb{R}^3$. Using suitable biorthogonal wavelet bases $\\Psi$, we introduce a new class of Besov-type spaces $B_{\\Psi,q}^\\alpha(L_p(\\partial \\Omega))$ of functions $u\\colon\\partial\\Omega\\rightarrow\\mathbb{C}$. 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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2734","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}