{"paper":{"title":"Approximate Solutions to Second Order Parabolic Equations I: analytic estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna L Mazzucato, Nick Costanzino, Radu Constantinescu, Victor Nistor","submitted_at":"2009-10-08T18:11:18Z","abstract_excerpt":"We establish a new type of local asymptotic formula for the Green's function ${\\mathcal G}_t(x,y)$ of a uniformly parabolic linear operator $\\partial_t - L$ with non-constant coefficients using dilations and Taylor expansions at a point $z=z(x,y)$, for a function $z$ with bounded derivatives such that $z(x,x)=x \\in {\\mathbb R}^N$. For $z(x,y) =x$, we recover the known, classical expansion obtained via pseudo-differential calculus. Our method is based on dilation at $z$, Dyson and Taylor series expansions, and the Baker-Campbell-Hausdorff commutator formula. Our procedure leads to an elementary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1562","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"}