{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FGHSTMOO4JVTP34ABM7PA34LQP","short_pith_number":"pith:FGHSTMOO","schema_version":"1.0","canonical_sha256":"298f29b1cee26b37ef800b3ef06f8b83f55efa0b7c8eff97288275fdba47a17d","source":{"kind":"arxiv","id":"1406.6162","version":1},"attestation_state":"computed","paper":{"title":"Radial symmetry and applications for a problem involving the $-\\Delta_p(\\cdot)$ operator and critical nonlinearity in~$\\mathbb{R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Berardino Sciunzi, Lucio Damascelli, Luigi Montoro, Susana Merchan","submitted_at":"2014-06-24T07:59:04Z","abstract_excerpt":"We consider weak non-negative solutions to the critical $p$-Laplace equation in $\\mathbb{R}^N$, $-\\Delta_p u =u^{p^*-1}$ in the singular case $1<p<2$. We prove that if the nonlinearity is locally Lipschitz continuous, namely $p^*\\geqslant2$ then all the solutions in ${\\mathcal D}^{1,p}(\\R^N)$ are radial (and radially decreasing) about some point."},"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":"1406.6162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-24T07:59:04Z","cross_cats_sorted":[],"title_canon_sha256":"b838a704a9d7dbad02d1c024f797735ca80511d7f0e145657a2d39c1642af8bb","abstract_canon_sha256":"be3d149686b39688459aaa66ffd4c87ee83f6592e8c8eaefab41df4f55312774"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:03.963717Z","signature_b64":"wNkM50wKLABzajNjuNx0e1BXJl7YKn1wbgnRyjU+CaC4mr8n06fBHzWnXoLYkjCtwoqgiZ48xSz9/7NnAMxvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"298f29b1cee26b37ef800b3ef06f8b83f55efa0b7c8eff97288275fdba47a17d","last_reissued_at":"2026-05-18T02:49:03.963326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:03.963326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Radial symmetry and applications for a problem involving the $-\\Delta_p(\\cdot)$ operator and critical nonlinearity in~$\\mathbb{R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Berardino Sciunzi, Lucio Damascelli, Luigi Montoro, Susana Merchan","submitted_at":"2014-06-24T07:59:04Z","abstract_excerpt":"We consider weak non-negative solutions to the critical $p$-Laplace equation in $\\mathbb{R}^N$, $-\\Delta_p u =u^{p^*-1}$ in the singular case $1<p<2$. We prove that if the nonlinearity is locally Lipschitz continuous, namely $p^*\\geqslant2$ then all the solutions in ${\\mathcal D}^{1,p}(\\R^N)$ are radial (and radially decreasing) about some point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6162","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.6162","created_at":"2026-05-18T02:49:03.963383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.6162v1","created_at":"2026-05-18T02:49:03.963383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6162","created_at":"2026-05-18T02:49:03.963383+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGHSTMOO4JVT","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGHSTMOO4JVTP34A","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGHSTMOO","created_at":"2026-05-18T12:28:28.263976+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/FGHSTMOO4JVTP34ABM7PA34LQP","json":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP.json","graph_json":"https://pith.science/api/pith-number/FGHSTMOO4JVTP34ABM7PA34LQP/graph.json","events_json":"https://pith.science/api/pith-number/FGHSTMOO4JVTP34ABM7PA34LQP/events.json","paper":"https://pith.science/paper/FGHSTMOO"},"agent_actions":{"view_html":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP","download_json":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP.json","view_paper":"https://pith.science/paper/FGHSTMOO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.6162&json=true","fetch_graph":"https://pith.science/api/pith-number/FGHSTMOO4JVTP34ABM7PA34LQP/graph.json","fetch_events":"https://pith.science/api/pith-number/FGHSTMOO4JVTP34ABM7PA34LQP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP/action/storage_attestation","attest_author":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP/action/author_attestation","sign_citation":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP/action/citation_signature","submit_replication":"https://pith.science/pith/FGHSTMOO4JVTP34ABM7PA34LQP/action/replication_record"}},"created_at":"2026-05-18T02:49:03.963383+00:00","updated_at":"2026-05-18T02:49:03.963383+00:00"}