{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EL2YHWOVHT5XPXNWNWW7BFKVDG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9aedb65f93c61ff5e16658a3d8a0ef182f09a193a7c47175f6d3bcaccc382c7a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T08:13:38Z","title_canon_sha256":"78b37ef9763f75aafee073065fdb3f832c39e94e4bc9ad78b02e6418dd711c25"},"schema_version":"1.0","source":{"id":"1605.01175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01175","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01175v2","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01175","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"EL2YHWOVHT5X","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EL2YHWOVHT5XPXNW","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EL2YHWOV","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:0409768ef61059c84e2f9155a7242cf5e9a6f6711816216d9bb5c15c397265a9","target":"graph","created_at":"2026-05-18T00:42:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We discuss several properties of eigenvalues and eigenfunctions of the $p$-Laplacian on a ball subject to zero Dirichlet boundary conditions. Among main results, in two dimensions, we show the existence of nonradial eigenfunctions which correspond to the radial eigenvalues. Also we prove the existence of eigenfunctions whose shape of the nodal set cannot occur in the linear case $p=2$. Moreover, the limit behavior of some eigenvalues as $p \\to 1+$ and $p \\to +\\infty$ is studied.","authors_text":"Pavel Drabek, Vladimir Bobkov","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T08:13:38Z","title":"On some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the $p$-Laplacian on a disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01175","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ff911d46490922698c01fb441f2d24ddea19843bfeeed36dd6edb40d8440dd8f","target":"record","created_at":"2026-05-18T00:42:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9aedb65f93c61ff5e16658a3d8a0ef182f09a193a7c47175f6d3bcaccc382c7a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T08:13:38Z","title_canon_sha256":"78b37ef9763f75aafee073065fdb3f832c39e94e4bc9ad78b02e6418dd711c25"},"schema_version":"1.0","source":{"id":"1605.01175","kind":"arxiv","version":2}},"canonical_sha256":"22f583d9d53cfb77ddb66dadf09555198285859d99b04632154f731fa930b961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22f583d9d53cfb77ddb66dadf09555198285859d99b04632154f731fa930b961","first_computed_at":"2026-05-18T00:42:44.422220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:44.422220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WkIiZ5675dOtaDKrTw54BHfrp14mYf04ylC8BzV88v5D5CKIo/GEZ7ox9rA7y3DZ3+phIU7/UgoByMdrqWLmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:44.422822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff911d46490922698c01fb441f2d24ddea19843bfeeed36dd6edb40d8440dd8f","sha256:0409768ef61059c84e2f9155a7242cf5e9a6f6711816216d9bb5c15c397265a9"],"state_sha256":"03b93cb959f77b47d47fe953d0f73b4ffac402d223aba4ea37073ce501e9827f"}