{"paper":{"title":"Homogenization and Orowan's law for anisotropic fractional operators of any order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Stefania Patrizi","submitted_at":"2016-10-01T23:17:36Z","abstract_excerpt":"We consider an anisotropic L\\'evy operator $\\mathcal{I}_s$ of any order $s\\in(0,1)$ and we consider the homogenization properties of an evolution equation.\n  The scaling properties and the effective Hamiltonian that we obtain is different according to the cases $s<1/2$ and $s>1/2$.\n  In the isotropic onedimensional case, we also prove a statement related to the so-called Orowan's law, that is an appropriate scaling of the effective Hamiltonian presents a linear behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00203","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"}