{"paper":{"title":"Coincidence sets in quasilinear elliptic problems of monostable type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shingo Takeuchi","submitted_at":"2010-09-16T06:53:21Z","abstract_excerpt":"This paper concerns the formation of a coincidence set for the positive solution of $p$-Laplacian elliptic problems of monostable type. It is proved that for any small parameter of diffusion term, the solution coincides with the stable zero-function $a(x)$ of reaction term in an open set if $a(x)$ is $p$-harmonic (but, not constant) and a zero of order less than 1. Inversely, it is also shown that the solution is less than $a(x)$ if $a(x)$ is a zero of order greater than or equal to 1. The proof rely on comparison theorems and an energy method for obtaining local comaprison functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3102","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"}