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Consider the divergence-form operator ${\\mathscr L}^{A}=-{\\rm div}(A\\nabla)$ with mixed boundary conditions on $\\Omega$. We extend the bilinear inequality that we proved in [16] in the special case when $\\Omega=\\mathbb{R}^{d}$. As a consequence, we obtain that the solution to the parabolic problem $u^{\\prime}(t)+{\\mathscr L}^{A}u(t)=f(t)$, $u(0)=0$, has maximal regularity in $L^{p}(\\Omega)$, for all $p>1$ such that $A$ satisf"},"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":"1905.01374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-03T22:39:05Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cd1e06e54850e48dec83de53027e819d227a915bb984d3146000e4b047c7890d","abstract_canon_sha256":"14eed26cce0509a9af8f6f098a9a46ecece294d6f1ac988ec00c66d8a148de74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:30.201608Z","signature_b64":"iOjUOh355NTwi8jon74qaU3iZLys/3UMXkeEtq3lW33b95d9zSPPWQo7b+RqtUNvyJ6ELt+hq3fWQThoZyTUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df603e16ac0a967c020f5b9be04d208ca5c835323865a731ab8cf6bdefc04650","last_reissued_at":"2026-05-17T23:39:30.200988Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:30.200988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilinear embedding for divergence-form operators with complex coefficients on irregular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Andrea Carbonaro, Oliver Dragi\\v{c}evi\\'c","submitted_at":"2019-05-03T22:39:05Z","abstract_excerpt":"Let $\\Omega\\subseteq \\mathbb{R}^{d}$ be open and $A$ a complex uniformly strictly accretive $d\\times d$ matrix-valued function on $\\Omega$ with $L^{\\infty}$ coefficients. 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As a consequence, we obtain that the solution to the parabolic problem $u^{\\prime}(t)+{\\mathscr L}^{A}u(t)=f(t)$, $u(0)=0$, has maximal regularity in $L^{p}(\\Omega)$, for all $p>1$ such that $A$ satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01374","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":"1905.01374","created_at":"2026-05-17T23:39:30.201080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.01374v2","created_at":"2026-05-17T23:39:30.201080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01374","created_at":"2026-05-17T23:39:30.201080+00:00"},{"alias_kind":"pith_short_12","alias_value":"35QD4FVMBKLH","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"35QD4FVMBKLHYAQP","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"35QD4FVM","created_at":"2026-05-18T12:33:07.085635+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/35QD4FVMBKLHYAQPLON6ATJARS","json":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS.json","graph_json":"https://pith.science/api/pith-number/35QD4FVMBKLHYAQPLON6ATJARS/graph.json","events_json":"https://pith.science/api/pith-number/35QD4FVMBKLHYAQPLON6ATJARS/events.json","paper":"https://pith.science/paper/35QD4FVM"},"agent_actions":{"view_html":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS","download_json":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS.json","view_paper":"https://pith.science/paper/35QD4FVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.01374&json=true","fetch_graph":"https://pith.science/api/pith-number/35QD4FVMBKLHYAQPLON6ATJARS/graph.json","fetch_events":"https://pith.science/api/pith-number/35QD4FVMBKLHYAQPLON6ATJARS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS/action/storage_attestation","attest_author":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS/action/author_attestation","sign_citation":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS/action/citation_signature","submit_replication":"https://pith.science/pith/35QD4FVMBKLHYAQPLON6ATJARS/action/replication_record"}},"created_at":"2026-05-17T23:39:30.201080+00:00","updated_at":"2026-05-17T23:39:30.201080+00:00"}