{"paper":{"title":"A Liouville theorem for high order degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Congming Li, Genggeng Huang","submitted_at":"2014-07-30T09:30:42Z","abstract_excerpt":"In this paper, we apply the moving plane method to the following high order degenerate elliptic equation,\\begin{equation*} (-A)^p u=u^\\alpha\\text{ in } \\mathbb R^{n+1}_+,n\\geq 1, \\end{equation*}where the operator $A=y\\partial_y^2+a\\partial_y+\\Delta_x,a\\geq 1$. We get a Liouville theorem for subcritical case and classify the solutions for the critical case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7978","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"}