{"paper":{"title":"Compact Embedding Theorem Associated with Classical Weight {Functions} in Two Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B.J. Nkwamouo, J.L. Woukeng, M.K. Nangho","submitted_at":"2026-05-14T11:56:10Z","abstract_excerpt":"For a classical weight function $\\rho$ defined on a simply connected open subset $\\Omega$ of $\\mathbb{R}^2$ (either bounded or unbounded) with piecewise $C^1$ boundary, we prove density and compact embedding of a matrix-weighted Sobolev space in the weighted Lebesgue space $L^2(\\Omega,\\, \\rho)$. As an application, we investigate {via a variational} method, eigenvalue problem of a degenerate Helmholtz operator on triangle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14732","kind":"arxiv","version":1},"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"}