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We establish the existence of a solution $u_\\lambda$ which exhibits a sharp boundary layer along the entire boundary $\\partial\\Omega$ as $\\lambda\\to 0$. These solutions have large mass in the sense that $ \\int_\\Omega \\lambda e^{u_\\lambda} \\sim |\\log\\lambda|.$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.2511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-11T09:21:32Z","cross_cats_sorted":[],"title_canon_sha256":"c4b9ab4f1ab028976169e2f67de9e2554ab401908ee7ce4e871f04f01a2c38e6","abstract_canon_sha256":"ee0cf49f4aa394c76b93e47f16cac54bb329d7979b7724169df38fc6dded6968"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:16.320900Z","signature_b64":"ljLBevgSufMZEFu9JGdK74xzMUT3I3BkjUglqXtJaiS+Tl/I2a6k+PVUJ7WPOviABPKwgm/QQpeTMczx57R7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b890f4b37c799241a0c86a22fe52428d8c1c9e4bc4d13e6ced791ecbccc6b7","last_reissued_at":"2026-05-18T01:19:16.320477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:16.320477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large mass boundary condensation patterns in the stationary Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Giusi Vaira, Manuel del Pino","submitted_at":"2014-03-11T09:21:32Z","abstract_excerpt":"We consider the boundary value problem $-\\Delta u + u =\\lambda e^u$ in $\\Omega$ with Neumann boundary condition, where $\\Omega$ is a bounded smooth domain in $\\mathbb R^2$, $\\lambda>0.$ This problem is equivalent to the stationary Keller-Segel system from chemotaxis. 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