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Sreenadh","submitted_at":"2019-06-25T16:16:42Z","abstract_excerpt":"In this article, we are study the following Dirichlet problem with Choquard type non linearity \\[ -\\Delta_{\\mathbb{H}} u = a u+ \\left(\\int_{\\Omega}\\frac{|u(\\eta)|^{Q^*_\\lambda}}{|\\eta^{-1}\\xi|^{\\lambda}}d\\eta\\right)|u|^{Q^*_\\lambda-2}u \\; \\text{in}\\; \\Omega,\\quad\n  u = 0 \\; \\text{ on } \\partial \\Omega , \\]\n  where $\\Omega$ is a smooth bounded subset of the Heisenberg group $\\mathbb{H}^N, N\\in \\mathbb N$ with $C^2$ boundary and $\\Delta_{\\mathbb{H}}$ is the Kohn Laplacian on the Heisenberg group $\\mathbb{H}^N$. Here, $Q^*_\\lambda=\\frac{2Q-\\lambda}{Q-2},\\; Q= 2N+2$ and $a$ is a positive real para"},"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":"1906.10628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-25T16:16:42Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a896c79a6e070fc82c32b2921eaa2ad5fc9345a23cf8754f3672d94ee08060df","abstract_canon_sha256":"f51010fbd1039f1caa1ec6a67d22a7947a4affb699b350c7f8969b5b719a52df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:52.741742Z","signature_b64":"oaNY43PFMKZp61qgr9fYMw6wGxLpmXw1RC7ioACcJhMzzwYPbVNJbLAx/1sVIA5osMymV6xoj+zyN3IUIuRXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2db4845733796d339fa27b677375738593c84fdbb1b538d13ca044ce1e5432cc","last_reissued_at":"2026-05-17T23:41:52.741257Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:52.741257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brezis-Nirenberg type result for Kohn Laplacian with critical Choquard Nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Divya Goel, K. Sreenadh","submitted_at":"2019-06-25T16:16:42Z","abstract_excerpt":"In this article, we are study the following Dirichlet problem with Choquard type non linearity \\[ -\\Delta_{\\mathbb{H}} u = a u+ \\left(\\int_{\\Omega}\\frac{|u(\\eta)|^{Q^*_\\lambda}}{|\\eta^{-1}\\xi|^{\\lambda}}d\\eta\\right)|u|^{Q^*_\\lambda-2}u \\; \\text{in}\\; \\Omega,\\quad\n  u = 0 \\; \\text{ on } \\partial \\Omega , \\]\n  where $\\Omega$ is a smooth bounded subset of the Heisenberg group $\\mathbb{H}^N, N\\in \\mathbb N$ with $C^2$ boundary and $\\Delta_{\\mathbb{H}}$ is the Kohn Laplacian on the Heisenberg group $\\mathbb{H}^N$. Here, $Q^*_\\lambda=\\frac{2Q-\\lambda}{Q-2},\\; Q= 2N+2$ and $a$ is a positive real para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10628","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":"1906.10628","created_at":"2026-05-17T23:41:52.741337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.10628v2","created_at":"2026-05-17T23:41:52.741337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10628","created_at":"2026-05-17T23:41:52.741337+00:00"},{"alias_kind":"pith_short_12","alias_value":"FW2IIVZTPFWT","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"FW2IIVZTPFWTHH5C","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"FW2IIVZT","created_at":"2026-05-18T12:33:15.570797+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/FW2IIVZTPFWTHH5CPNTXG5LTQW","json":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW.json","graph_json":"https://pith.science/api/pith-number/FW2IIVZTPFWTHH5CPNTXG5LTQW/graph.json","events_json":"https://pith.science/api/pith-number/FW2IIVZTPFWTHH5CPNTXG5LTQW/events.json","paper":"https://pith.science/paper/FW2IIVZT"},"agent_actions":{"view_html":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW","download_json":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW.json","view_paper":"https://pith.science/paper/FW2IIVZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.10628&json=true","fetch_graph":"https://pith.science/api/pith-number/FW2IIVZTPFWTHH5CPNTXG5LTQW/graph.json","fetch_events":"https://pith.science/api/pith-number/FW2IIVZTPFWTHH5CPNTXG5LTQW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW/action/storage_attestation","attest_author":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW/action/author_attestation","sign_citation":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW/action/citation_signature","submit_replication":"https://pith.science/pith/FW2IIVZTPFWTHH5CPNTXG5LTQW/action/replication_record"}},"created_at":"2026-05-17T23:41:52.741337+00:00","updated_at":"2026-05-17T23:41:52.741337+00:00"}