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Specifically, we show that if $\\xi$ is $\\alpha$-H\\\"{o}lder continuous and $f$ is $\\beta$-H\\\"{o}lder continuous then any viscosity solution is locally $\\gamma$-H\\\"{o}lder continuous for any $\\gamma<\\gamma_\\circ $, where \\[ \\gamma_\\circ=\\left\\{\\begin{array}{lll} \\min\\{1, \\frac{sp+\\alpha\\wedge\\beta}{p"},"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":"2507.09920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-14T04:57:56Z","cross_cats_sorted":[],"title_canon_sha256":"de5cc631d1cce1f432f3ae4388376f78ed62f126fbe7cf9ac3f5ea3ca20f2b35","abstract_canon_sha256":"2ae166bf650b11b10b1b7f7fdeb6efec60b7f84df6bfd428221d77309ea641f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:42.198786Z","signature_b64":"xn5vNsuUtxYImIgVSLy5M7LPjhMbikS+xYQS+NFfWa8qYl5n5lWKbykkprLm7Ts/CtDt5KQAHAwyIwIPcQRMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10be3ab657146505922e194bd967b2e3d949991dea8eba72c463ac1a2f1d2f04","last_reissued_at":"2026-07-05T11:36:42.198204Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:42.198204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved H\\\"older regularity of fractional $(p,q)$-Poisson equation with regular data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aniket Sen, Anup Biswas","submitted_at":"2025-07-14T04:57:56Z","abstract_excerpt":"We prove a quantitative H\\\"{o}lder continuity result for viscosity solutions to the equation $$ (-\\Delta_p)^{s}u(x) + {\\rm PV} \\int_{\\mathbb{R}^n} |u(x)-u(x+z)|^{q-2}(u(x)-u(x+z))\\frac{\\xi(x,z)}{|z|^{n+ tq}} dz=f \\quad \\text{in}\\; B_2, $$ where $t, s\\in (0, 1), 1<p\\leq q, tq\\leq sp$ and $\\xi\\geq 0$. 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