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In particular, structural conditions on $F$ are presented which ensure that $W^{2,n}(B_1)$ solutions achieve the optimal $C^{1,1}(B_{1/2})$ regularity when $f$ is H\\\"older continuous. Moreover, if $f$ is positive on $\\overline B_1$, Lipschitz continuous, and $\\{u\\neq 0\\} \\subset \\Omega$, then we obtain local $C^1$ regularity"},"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":"1403.4300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-17T23:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"cccb5a9364c81eeca65e3bafee559534da001fe981f404be09cb120b0ec77bd6","abstract_canon_sha256":"e74ba8d9c8523cff13e0e4d7f8f740823804530329881b2510a39f5f3088cdb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:41.578481Z","signature_b64":"qfSToWHJJaA8YRDMvnTMS63pltHPnhcvWvW31gKJ1coVtNazFYp7LsYoO0UHQdqxOgQ/NPPy9kmnnPwNzFNPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5541aac3057664e00b5913673a46acb1fcba2181ac1d994241d8cfa80fae6909","last_reissued_at":"2026-05-18T00:28:41.577753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:41.577753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Minne, Emanuel Indrei","submitted_at":"2014-03-17T23:00:40Z","abstract_excerpt":"We consider fully nonlinear obstacle-type problems of the form \\begin{equation*} \\begin{cases} F(D^{2}u,x)=f(x) & \\text{a.e. in}B_{1}\\cap\\Omega,|D^{2}u|\\le K & \\text{a.e. in}B_{1}\\backslash\\Omega, \\end{cases} \\end{equation*} where $\\Omega$ is an unknown open set and $K>0$. In particular, structural conditions on $F$ are presented which ensure that $W^{2,n}(B_1)$ solutions achieve the optimal $C^{1,1}(B_{1/2})$ regularity when $f$ is H\\\"older continuous. 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