{"paper":{"title":"Analysis of degenerate elliptic operators of Grushin type","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, Derek W. Robinson","submitted_at":"2006-07-24T00:16:14Z","abstract_excerpt":"We analyze degenerate, second-order, elliptic operators $H$ in divergence form on $L_2({\\bf R}^{n}\\times{\\bf R}^{m})$. We assume the coefficients are real symmetric and $a_1H_\\delta\\geq H\\geq a_2H_\\delta$ for some $a_1,a_2>0$ where \\[ H_\\delta=-\\nabla_{x_1} c_{\\delta_1, \\delta'_1}(x_1) \\nabla_{x_1}-c_{\\delta_2, \\delta'_2}(x_1) \\nabla_{x_2}^2 . \\] Here $x_1\\in{\\bf R}^n$, $x_2\\in{\\bf R}^m$ and $c_{\\delta_i, \\delta'_i}$ are positive measurable functions such that $c_{\\delta_i, \\delta'_i}(x)$ behaves like $|x|^{\\delta_i}$ as $x\\to0$ and $|x|^{\\delta_i'}$ as $x\\to\\infty$ with $\\delta_1,\\delta_1'\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607584","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"}