{"paper":{"title":"Stratification of free boundary points for a two-phase variational problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram L. Karakhanyan, Serena Dipierro","submitted_at":"2015-08-29T13:18:45Z","abstract_excerpt":"In this paper we study the two-phase Bernoulli type free boundary problem arising from the minimization of the functional $$ J(u):=\\int_{\\Omega}|\\nabla u|^p +\\lambda_+^p\\,\\chi_{\\{u>0\\}} +\\lambda_-^p\\,\\chi_{\\{u\\le 0\\}}, \\quad 1<p<\\infty. $$ Here $\\Omega \\subset \\R^N$ is a bounded smooth domain and $\\lambda_\\pm$ are positive constants such that $\\lambda_+^p-\\lambda^p_->0$. We prove the following dichotomy: if $x_0$ is a free boundary point then either the free boundary is smooth near $x_0$ or $u$ has linear growth at $x_0$. Furthermore, we show that for $p>1$ the free boundary has locally finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07447","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"}