{"paper":{"title":"Second-order operators with degenerate coefficients","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, A.F.M. ter Elst, Derek W. Robinson, Yueping Zhu","submitted_at":"2006-01-13T02:53:29Z","abstract_excerpt":"We consider properties of second-order operators $H = -\\sum^d_{i,j=1} \\partial_i \\, c_{ij} \\, \\partial_j$ on $\\Ri^d$ with bounded real symmetric measurable coefficients. We assume that $C = (c_{ij}) \\geq 0$ almost everywhere, but allow for the possibility that $C$ is singular. We associate with $H$ a canonical self-adjoint viscosity operator $H_0$ and examine properties of the viscosity semigroup $S^{(0)}$ generated by $H_0$. The semigroup extends to a positive contraction semigroup on the $L_p$-spaces with $p \\in [1,\\infty]$. We establish that it conserves probability, satisfies $L_2$~off-dia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601307","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"}