{"paper":{"title":"Homogenization of generalized second-order elliptic difference operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandre B. Simas, Fabio J. Valentim","submitted_at":"2015-08-14T03:56:46Z","abstract_excerpt":"Fix a function $W(x_1,\\ldots,x_d) = \\sum_{k=1}^d W_k(x_k)$ where each $W_k: \\mathbb{R} \\to \\mathbb{R}$ is a strictly increasing right continuous function with left limits. For a diagonal matrix function $A$, let $\\nabla A \\nabla_W = \\sum_{k=1}^d \\partial_{x_k}(a_k\\partial_{W_k})$ be a generalized second-order differential operator. We are interested in studying the homogenization of generalized second-order difference operators, that is, we are interested in the convergence of the solution of the equation $$\\lambda u_N - \\nabla^N A^N \\nabla_W^N u_N = f^N$$ to the solution of the equation $$\\la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03414","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"}