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We consider the problem of finding $u\\in K^s$, such that,\n  \\begin{equation*}\n  \\int_{\\mathbb{R}^d}{\\boldsymbol{a}(x,u,D^s u)\\cdot D^s(v-u)}\\,dx+\\int_\\Omega{b(x,u,D^s u)(v-u)}\\,dx\\geq 0 %\\langle F, v-u\\rangle\n  \\end{equation*} for all $v\\in K^s$. Here $K^s\\subset\\Lambda^{s,p}_0(\\Omega)$ is a non-empty, closed and convex set of a fractional Sobolev ty"},"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":"2311.18428","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-11-30T10:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"6971df1a4333e8abd5fcec11d31bd1f2f925c539a597544b0db9ea767652f4bf","abstract_canon_sha256":"1124da9c85fdf31d435e39dacf2aa0b59180fc544c2119ef814505f4d2b53b24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:18:42.255377Z","signature_b64":"/q4zLZqLsmhhek9dynukdsSHqW9rrlsrUMko6tTv4DVQitlL0BUpFDq3gWiUElUn9ttG7pRPEpaQ/f1zd/NeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67b022d2bd6d599cca3da36c060d9e3e47a9792767c831a139a0269f883c6793","last_reissued_at":"2026-07-05T07:18:42.255055Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:18:42.255055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unilateral Problems for Quasilinear Operators with Fractional Riesz Gradients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e Francisco Rodrigues, Pedro Miguel Campos","submitted_at":"2023-11-30T10:25:53Z","abstract_excerpt":"In this work, we develop the classical theory of monotone and pseudomonotone operators in the class of convex constrained Dirichlet-type problems involving fractional Riesz gradients in bounded and in unbounded domains $\\Omega\\subset\\mathbb{R}^d$. We consider the problem of finding $u\\in K^s$, such that,\n  \\begin{equation*}\n  \\int_{\\mathbb{R}^d}{\\boldsymbol{a}(x,u,D^s u)\\cdot D^s(v-u)}\\,dx+\\int_\\Omega{b(x,u,D^s u)(v-u)}\\,dx\\geq 0 %\\langle F, v-u\\rangle\n  \\end{equation*} for all $v\\in K^s$. Here $K^s\\subset\\Lambda^{s,p}_0(\\Omega)$ is a non-empty, closed and convex set of a fractional Sobolev ty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.18428","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/2311.18428/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":"2311.18428","created_at":"2026-07-05T07:18:42.255102+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.18428v1","created_at":"2026-07-05T07:18:42.255102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.18428","created_at":"2026-07-05T07:18:42.255102+00:00"},{"alias_kind":"pith_short_12","alias_value":"M6YCFUV5NVMZ","created_at":"2026-07-05T07:18:42.255102+00:00"},{"alias_kind":"pith_short_16","alias_value":"M6YCFUV5NVMZZSR5","created_at":"2026-07-05T07:18:42.255102+00:00"},{"alias_kind":"pith_short_8","alias_value":"M6YCFUV5","created_at":"2026-07-05T07:18:42.255102+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.06346","citing_title":"On generalized Sobolev-Orlicz spaces associated to the Riesz fractional gradient","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ","json":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ.json","graph_json":"https://pith.science/api/pith-number/M6YCFUV5NVMZZSR5UNWAMDM6HZ/graph.json","events_json":"https://pith.science/api/pith-number/M6YCFUV5NVMZZSR5UNWAMDM6HZ/events.json","paper":"https://pith.science/paper/M6YCFUV5"},"agent_actions":{"view_html":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ","download_json":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ.json","view_paper":"https://pith.science/paper/M6YCFUV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.18428&json=true","fetch_graph":"https://pith.science/api/pith-number/M6YCFUV5NVMZZSR5UNWAMDM6HZ/graph.json","fetch_events":"https://pith.science/api/pith-number/M6YCFUV5NVMZZSR5UNWAMDM6HZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ/action/storage_attestation","attest_author":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ/action/author_attestation","sign_citation":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ/action/citation_signature","submit_replication":"https://pith.science/pith/M6YCFUV5NVMZZSR5UNWAMDM6HZ/action/replication_record"}},"created_at":"2026-07-05T07:18:42.255102+00:00","updated_at":"2026-07-05T07:18:42.255102+00:00"}