{"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 $\\xi\\geq 0$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09920","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/2507.09920/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"}