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We establish a compactness result for the following class of subcritical/critical problems\n  \\begin{equation}\\label{sub_pro_abstract}\\tag{$\\mathcal{P}_{p_n}$}\n  -\\Delta u+(-\\Delta)^s"},"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":"2605.25157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-24T16:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"fb172b17b1333de103c84678fe66ce72f99b3ca9170213051d75b348c823b7ab","abstract_canon_sha256":"252f5a52fe46f3e5aa2bb001d0539454e4ca88634ace40e240b708ad84918edc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:20.657355Z","signature_b64":"ctvYjAWrvQnJpVyDkPWoBuOeMEK79kuNI9eCXkmtICkEql50cQ7I+Po/4wriaNgjaJByZXXe95pXsCAAz816Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a79e30fdfd7794ea2fb609ca974a460dd96c59f70017fc04b0ca4c33ef66e64","last_reissued_at":"2026-05-26T02:04:20.656796Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:20.656796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mousomi Bhakta, Nirjan Biswas, Paramananda Das","submitted_at":"2026-05-24T16:28:54Z","abstract_excerpt":"In this paper, we consider the following mixed local nonlocal Brezis-Nirenberg problem \\begin{equation}\\label{crit_pro_abstract}\\tag{$\\mathcal{P}_{2^*}$} -\\Delta u+(-\\Delta)^s u=\\lambda |u|^{p-2}u+|u|^{2^*-2}u\\text{ in }\\Omega,\\quad u=0\\text{ in }\\mathbb{R}^N \\setminus \\Omega, \\end{equation} where $\\Omega\\subset\\mathbb{R}^N$ is a bounded domain, $N\\geq3$, $s\\in(0,1)$, $\\lambda>0$, and $2\\leq p<2^*=\\frac{2N}{N-2}$. We establish a compactness result for the following class of subcritical/critical problems\n  \\begin{equation}\\label{sub_pro_abstract}\\tag{$\\mathcal{P}_{p_n}$}\n  -\\Delta u+(-\\Delta)^s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25157","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25157/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.25157","created_at":"2026-05-26T02:04:20.656897+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25157v1","created_at":"2026-05-26T02:04:20.656897+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25157","created_at":"2026-05-26T02:04:20.656897+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJ46GD67254U","created_at":"2026-05-26T02:04:20.656897+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJ46GD67254U5IX3","created_at":"2026-05-26T02:04:20.656897+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJ46GD67","created_at":"2026-05-26T02:04:20.656897+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/RJ46GD67254U5IX3MCOKS5FEMD","json":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD.json","graph_json":"https://pith.science/api/pith-number/RJ46GD67254U5IX3MCOKS5FEMD/graph.json","events_json":"https://pith.science/api/pith-number/RJ46GD67254U5IX3MCOKS5FEMD/events.json","paper":"https://pith.science/paper/RJ46GD67"},"agent_actions":{"view_html":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD","download_json":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD.json","view_paper":"https://pith.science/paper/RJ46GD67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25157&json=true","fetch_graph":"https://pith.science/api/pith-number/RJ46GD67254U5IX3MCOKS5FEMD/graph.json","fetch_events":"https://pith.science/api/pith-number/RJ46GD67254U5IX3MCOKS5FEMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD/action/storage_attestation","attest_author":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD/action/author_attestation","sign_citation":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD/action/citation_signature","submit_replication":"https://pith.science/pith/RJ46GD67254U5IX3MCOKS5FEMD/action/replication_record"}},"created_at":"2026-05-26T02:04:20.656897+00:00","updated_at":"2026-05-26T02:04:20.656897+00:00"}