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In particular, we extend the existence, regularity and Wolff potential estimates for SOLA (Solutions Obtained as Limits of Approximations), established by Kuusi, Mingione, and Sire (Comm. Math. Phys. 337(3):1317--1368, 2015), to the strongly singular case $1 < p \\le 2-s/n$. Moreover, using Wolff potentials and Orlicz capacities, we"},"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":"2405.11747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-20T03:13:00Z","cross_cats_sorted":[],"title_canon_sha256":"7695730dbc85b27e80fe311a0f217dd536c60286cb837bbf3ab01e996d73d722","abstract_canon_sha256":"24ab067b780e442088bf99ab5b22fb2ae098bd4a285078958299958a3b769308"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:06:59.396019Z","signature_b64":"lno22x0r0Mq/AQTe55ALrqPR6PWzVlbwzUh2EVMCMBiv7VA1TFbt0/Hai191OC80RGNU67vmfpG0I4vwW31tBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2546f9ba3e679f45bdce9ff2042c61fe0e795204af23f5b29deafcfaa440ce08","last_reissued_at":"2026-06-09T02:06:59.395064Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:06:59.395064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wolff potentials and nonlocal equations of Lane-Emden type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jihoon Ok, Kyeong Song, Quoc-Hung Nguyen","submitted_at":"2024-05-20T03:13:00Z","abstract_excerpt":"We consider nonlocal equations of the type \\[ (-\\Delta_{p})^{s}u = \\mu \\quad \\text{in}\\;\\; \\Omega, \\] where $\\Omega \\subset \\mathbb{R}^{n}$ is either a bounded domain or the whole $\\mathbb{R}^{n}$, $\\mu$ is a Radon measure on $\\Omega$, $0 < s < 1$ and $1 < p < n/s$. In particular, we extend the existence, regularity and Wolff potential estimates for SOLA (Solutions Obtained as Limits of Approximations), established by Kuusi, Mingione, and Sire (Comm. Math. Phys. 337(3):1317--1368, 2015), to the strongly singular case $1 < p \\le 2-s/n$. 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