{"paper":{"title":"Uniform subellipticity","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, Derek W. Robinson","submitted_at":"2006-12-22T04:16:47Z","abstract_excerpt":"We establish two global subellipticity properties of positive symmetric second-order partial differential operators on $L_2(\\Ri^d)$. First, if $m \\in \\Ni$ then we consider operators $H_0$ with coefficients in $W^{m+1,\\infty}(\\Ri^d)$ and domain $D(H_0)=W^{\\infty,2}(\\Ri^d)$ satisfying the subellipticity property \\[ c (\\phi, (I+H_0)\\phi)\\geq \\|\\Delta^{\\gamma/2} \\phi\\|_2^2 \\] for some $c>0$ and $\\gamma\\in<0,1]$, uniformly for all $\\phi\\in W^{\\infty,2}(\\Ri^d)$, where $\\Delta$ denotes the usual Laplacian. Then we prove that $D(H^\\alpha) \\subseteq D(\\Delta^{\\alpha \\gamma})$ for all $\\alpha \\in [0,2^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612680","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"}