{"paper":{"title":"On the mixed Cauchy problem with data on singular conics","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Hermann Render, Peter Ebenfelt","submitted_at":"2007-03-04T17:56:13Z","abstract_excerpt":"We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators whose principal part $Q_{2p}(D)$ essentially is the (complex) Laplace operator to a power, $\\Delta^p$. We pose inital data on a singular conic divisor given by P=0, where $P$ is a homogeneous polynomial of degree $2p$. We show that this problem is uniquely solvable if the polynomial $P$ is elliptic, in a certain sense, with respect to the principal part $Q_{2p}(D)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703110","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"}