{"paper":{"title":"Anisotropic Finsler $N$-Laplacian Liouville equation in convex cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changfeng Gui, Wei Dai, Yunpeng Luo","submitted_at":"2024-07-06T07:45:52Z","abstract_excerpt":"We consider the anisotropic Finsler $N$-Laplacian Liouville equation \\[-\\Delta ^{H}_{N}u=e^u \\qquad {\\rm{in}}\\,\\, \\mathcal{C},\\] where $N\\geq2$, $\\mathcal{C}\\subseteq\\mathbb{R}^{N}$ is an open convex cone including $\\mathbb{R}^{N}$, the half space $\\mathbb{R}^{N}_{+}$ and $\\frac{1}{2^{m}}$-space $\\mathbb{R}^{N}_{2^{-m}}:=\\{x\\in\\mathbb{R}^{N}\\mid x_{1},\\cdots,x_{m}>0\\}$ ($m=1,\\cdots,N$), and the anisotropic Finsler $N$-Laplacian $\\Delta ^{H}_{N}$ is induced by a positively homogeneous function $H(x)$ of degree $1$. All solutions to the Finsler $N$-Laplacian Liouville equation with finite mass a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.04987","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.04987/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}