{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RKGRYBLSSVVJBKBLILGPSUZ7B7","short_pith_number":"pith:RKGRYBLS","schema_version":"1.0","canonical_sha256":"8a8d1c0572956a90a82b42ccf9533f0ff47a8304c7b4f019e063b7f4a6c14069","source":{"kind":"arxiv","id":"1509.01731","version":2},"attestation_state":"computed","paper":{"title":"A note on the local regularity of distributional solutions and subsolutions of semilinear elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2015-09-05T20:03:09Z","abstract_excerpt":"In this note we prove local regularity results for distributional solutions and subsolutions of semilinear elliptic systems such as $$ L_k^m u_k = f_k(x,u_1,\\ldots,u_N) \\quad\\text{in }\\mathbb{R}^n\\qquad (k=1,\\ldots,N) $$ where $L_1,\\ldots,L_N$ are of divergence-form and $n\\geq 2m$. We show that distributional subsolutions are locally bounded from above if $|f_k(x,z)|\\leq C(1+|z|^p)$ for $1\\leq p<\\frac{n}{n-2m},k=1,\\ldots,N$.\n  Furthermore, regularity properties of subsolutions and improved versions for bounded subsolutions are given. Even for $f_1=\\ldots=f_N=0$ our results are new."},"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":"1509.01731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-05T20:03:09Z","cross_cats_sorted":[],"title_canon_sha256":"c715793c8d552b650c322d28fa742b4e0a94f054b2a30c09ccaccacf130e44c1","abstract_canon_sha256":"5a3814d27a6432159b56f1b1185a92ed76f17cf05f6b01e16430aabce96024cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:34.149230Z","signature_b64":"82Qp+lwDCaPhPEBVwybJbK0tV6dybGr50SJFkh5sHdg0v7BbzI4CYSm5rQm0pr8aC44ZNew+i9Rim4MekM3WDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a8d1c0572956a90a82b42ccf9533f0ff47a8304c7b4f019e063b7f4a6c14069","last_reissued_at":"2026-05-18T01:19:34.148746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:34.148746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the local regularity of distributional solutions and subsolutions of semilinear elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2015-09-05T20:03:09Z","abstract_excerpt":"In this note we prove local regularity results for distributional solutions and subsolutions of semilinear elliptic systems such as $$ L_k^m u_k = f_k(x,u_1,\\ldots,u_N) \\quad\\text{in }\\mathbb{R}^n\\qquad (k=1,\\ldots,N) $$ where $L_1,\\ldots,L_N$ are of divergence-form and $n\\geq 2m$. We show that distributional subsolutions are locally bounded from above if $|f_k(x,z)|\\leq C(1+|z|^p)$ for $1\\leq p<\\frac{n}{n-2m},k=1,\\ldots,N$.\n  Furthermore, regularity properties of subsolutions and improved versions for bounded subsolutions are given. Even for $f_1=\\ldots=f_N=0$ our results are new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01731","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.01731","created_at":"2026-05-18T01:19:34.148831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01731v2","created_at":"2026-05-18T01:19:34.148831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01731","created_at":"2026-05-18T01:19:34.148831+00:00"},{"alias_kind":"pith_short_12","alias_value":"RKGRYBLSSVVJ","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RKGRYBLSSVVJBKBL","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RKGRYBLS","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7","json":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7.json","graph_json":"https://pith.science/api/pith-number/RKGRYBLSSVVJBKBLILGPSUZ7B7/graph.json","events_json":"https://pith.science/api/pith-number/RKGRYBLSSVVJBKBLILGPSUZ7B7/events.json","paper":"https://pith.science/paper/RKGRYBLS"},"agent_actions":{"view_html":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7","download_json":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7.json","view_paper":"https://pith.science/paper/RKGRYBLS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01731&json=true","fetch_graph":"https://pith.science/api/pith-number/RKGRYBLSSVVJBKBLILGPSUZ7B7/graph.json","fetch_events":"https://pith.science/api/pith-number/RKGRYBLSSVVJBKBLILGPSUZ7B7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7/action/storage_attestation","attest_author":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7/action/author_attestation","sign_citation":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7/action/citation_signature","submit_replication":"https://pith.science/pith/RKGRYBLSSVVJBKBLILGPSUZ7B7/action/replication_record"}},"created_at":"2026-05-18T01:19:34.148831+00:00","updated_at":"2026-05-18T01:19:34.148831+00:00"}