{"paper":{"title":"A matrix-based spectral method for the numerical approximation of the fractional Laplacian and the fractional $p$-Laplacian of functions defined on $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Carlota M. Cuesta, Francisco de la Hoz, Lo\\\"ic Constantin","submitted_at":"2026-05-22T05:54:44Z","abstract_excerpt":"Given a function $u$ defined on $\\mathbb R^n$, its fractional $p$-Laplacian is given by $$(-\\Delta)_p^su(\\vec x)=C_1(n,s,p)\\int_{\\mathbb R^n}\\frac{|u(\\vec x)-u(\\vec y)|^{p-2}(u(\\vec x)-u(\\vec y))}{\\|\\vec x-\\vec y\\|_2^{n+sp}}d\\vec y,\\quad\\vec x\\in\\mathbb R^n,$$where the integral is understood in the principal value sense, $p\\in(1,\\infty)$, $s\\in(0,1)$, and $C_1(n,s,p)$ is a normalization constant. A formally equivalent nonlinear Balakrishnan formulation is given by $$(-\\Delta)_p^su(\\vec x)=C_4(n,s,p)\\int_0^\\infty\\Delta(t-\\Delta)^{-1}\\left[\\Phi_p(u(\\vec x)-u(\\cdot))\\right](\\vec x)\\frac{dt}{t^{1-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23252","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/2605.23252/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"}