{"paper":{"title":"The unique continuation property for a nonlinear equation on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carolina A. Mosquera, Julio D. Rossi, Leandro M. Del Pezzo","submitted_at":"2012-03-18T19:10:03Z","abstract_excerpt":"In this paper we study the game $p-$Laplacian on a tree, that is, $$ u(x)=\\frac{\\alpha}2\\left\\{\\max_{y\\in \\S(x)}u(y) + \\min_{y\\in \\S(x)}u(y)\\right\\} + \\frac{\\beta}{m}\\sum_{y\\in \\S(x)} u(y), $$ here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$.\n  We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets $U$ such that $u\\mid_U=0$ implies $u \\equiv 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3989","kind":"arxiv","version":3},"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"}