{"paper":{"title":"Structure of singularities in the nonlinear nerve conduction problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram Karakhanyan","submitted_at":"2019-06-12T21:27:54Z","abstract_excerpt":"We give a characterisation of the singular points of the free boundary $\\partial \\{u>0\\}$ for viscosity solutions of the nonlinear equation \\begin{equation}F(D^2 u)=-\\chi_{\\{u>0\\}},\\tag{0.1} \\end{equation} where $F$ is a fully nonlinear elliptic operator and $\\chi$ the characteristic function. The equation (0.1) models the propagation of a nerve impulse along an axon.\n  We analyse the structure of the free boundary $\\partial\\{ u>0\\}$ near the singular points where $u$ and $\\nabla u$ vanish simultaneously. Our method uses the stratification approach developed in [DK18].\n  In particular, when $n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05383","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":""},"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"}