{"paper":{"title":"On complex singularity analysis for some linear partial differential equations in $\\mathbb{C}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Alberto Lastra, Catherine Stenger, St\\'ephane Malek","submitted_at":"2013-04-01T11:26:40Z","abstract_excerpt":"We investigate the existence of local holomorphic solutions $Y$ of linear partial differential equations in three complex variables whose coefficients are singular along an analytic variety $\\Theta$ in $\\mathbb{C}^{2}$. The coefficients are written as linear combinations of powers of a solution $X$ of some first order nonlinear partial differential equation following an idea we have initiated in a previous work \\cite{mast}. The solutions $Y$ are shown to develop singularities along $\\Theta$ with estimates of exponential type depending on the growth's rate of $X$ near the singular variety. We c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0334","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"}